First of all, we must observe that all proper mathematical judgments are a priori, and not empirical, because they carry with them necessity, which cannot be obtained from experience. But if this be not conceded to me, very good; I shall confine my assertion pure Mathematics, the very notion of which implies that it contains pure a priori and not empirical cognitions.
It might at first be thought that the proposition 7 + 5 = 12 is a mere analytical judgment, following from the concept of the sum of seven and five, according to the law of contradiction. But on closer examination it appears that the concept of the sum of 7+5 contains merely their union in a single number, without its being at all thought what the particular number is that unites them. The concept of twelve is by no means thought by merely thinking of the combination of seven and five; and analyze this possible sum as we may, we shall not discover twelve in the concept. We must go beyond these concepts, by calling to our aid some concrete image [Anschauung], i.e., either our five fingers, or five points (as Segner has it in his Arithmetic), and we must add successively the units of the five, given in some concrete image [Anschauung], to the concept of seven. Hence our concept is really amplified by the proposition 7 + 5 = 12, and we add to the first a second, not thought in it. Arithmetical judgments are therefore synthetical, and the more plainly according as we take larger numbers; for in such cases it is clear that, however closely we analyze our concepts without calling visual images (Anscliauung) to our aid, we can never find the sum by such mere dissection.

The most important aspect of understanding Kantian epistemology with respect to the AfM is that moral claims are simply synthetic a priori propositions. In other words, there is no epistemic distinction between some kinds of synthetic a priori judgments (i.e., moral judgments) and others (i.e., mathematics). Three citations from Kant should suffice:
a. In the Groundwork of the Metaphysics of Morals (reasonably readable, for Kant), Kant explains that moral principles are fully defined by the concept of synthetic a priori judgments, just as in mathematics:

Kant 1:
[T]hese principles are to be found altogether a priori, free from everything empirical, in pure rational concepts only and nowhere else, not even in the smallest degree; then rather to adopt the method of making this a separate inquiry, as pure practical philosophy, or (if one may use a name so decried) as metaphysic of morals,(*) to bring it by itself to completeness, and to require the public, which wishes for popular treatment, to await the issue of this undertaking.
(*) Just as pure mathematics are distinguished from applied, pure logic from applied, so if we choose we may also distinguish pure philosophy of morals (metaphysic) from applied (viz., applied to human nature). By this designation we are also at once reminded that moral principles are not based on properties of human nature, but must subsist a priori of themselves, while from such principles practical rules must be capable of being deduced for every rational nature, and accordingly for that of man.

b. Later, Kant refutes the false distinction that mathematical synthetic a priori statements somehow aren't “prescriptive” whereas moral judgments are.

Kant 2:
Now arises the question, how are all these imperatives possible? This question does not seek to know how we can conceive the accomplishment of the action which the imperative ordains, but merely how we can conceive the obligation of the will which the imperative expresses. No special explanation is needed to show how an imperative of skill is possible. Whoever wills the end, wills also (so far as reason decides his conduct) the means in his power which are indispensably necessary thereto. This proposition is, as regards the volition, analytical; for, in willing an object as my effect, there is already thought the causality of myself as an acting cause, that is to say, the use of the means; and the imperative reduces from the conception of volition of an end the conception of actions necessary to this end. Synthetical propositions must no doubt be employed in defining the means to a proposed end; but they do not concern the principle, the act of the will, but the object and its realization. E.g., that in order to bisect a line on an unerring principle I must draw from its extremities two intersecting arcs; this no doubt is taught by mathematics only in synthetical propositions; but if I know that it is only by this process that the intended operation can be performed, then to say that, if I fully will the operation, I also will the action required for it, is an analytical proposition; for it is one and the same thing to conceive something as an effect which I can produce in a certain way, and to conceive myself as acting in this way.

c. Thus, Kant concludes, the Categorical Imperative is a synthetic, a priori judgment.

Kant 3:
We shall therefore have to investigate a priori the possibility of a categorical imperative, as we have not in this case the advantage of its reality being given in experience, so that [the elucidation of] its possibility should be requisite only for its explanation, not for its establishment. In the meantime it may be discerned beforehand that the categorical imperative alone has the purport of a practical law; all the rest may indeed be called principles of the will but not laws, since whatever is only necessary for the attainment of some arbitrary purpose may be considered as in itself contingent, and we can at any time be free from the precept if we give up the purpose; on the contrary, the unconditional command leaves the will no liberty to choose the opposite; consequently it alone carries with it that necessity which we require in a law.

Secondly, in the case of this categorical imperative or law of morality, the difficulty (of discerning its possibility) is a very profound one. It is an a priori synthetical practical proposition;(*) and as there is so much difficulty in discerning the possibility of speculative propositions of this kind, it may readily be supposed that the difficulty will be no less with the practical.
(*) I connect the act with the will without presupposing any condition resulting from any inclination, but a priori, and therefore necessarily (though only objectively, i.e., assuming the idea of a reason possessing full power over all subjective motives). This is accordingly a practical proposition which does not deduce the willing of an action by mere analysis from another already presupposed (for we have not such a perfect will), but connects it immediately with the conception of the will of a rational being, as something not contained in it.

To try and simplify: for Kant, all synthetic a priori judgments are “prescriptive,” because they are “unconditional commands” that give our minds “no liberty to choose the opposite.” I cannot will myself to believe that 7 + 5 = 238; it thus operates as a “command” equal in force to moral imperatives.
Applying those imperatives to particular situations is, as Kant suggests in Kant 2 above, simply an operation of our contingent practical faculties; that's what he means when he says that “whoever wills the end, wills also the means in his power which are indispensably necessary thereto.”
I know this is tough stuff, but the bottom line is that the prerequisites to “objective morality” are simply: (1) the ability to ascertain moral truths a priori, which Kant shows is possible without any external referent, and (2) the subjective and contingent condition of the human brain to carry out the will. No third party is necessary.
For Kant, then, I recognize that lying is wrong in exactly the same way that I recognize that the proposition 7 + 5 = 238 is wrong. I may nonetheless choose to lie anyway for personal gain recognizing that my action contradicts my will. Similarly, I may choose to act on 7 + 5 = 238 for personal gain — e.g., in filling out my deductions on my income tax — and I similarly recognize that I have willed an internal contradiction. Thus, one of Kant's major contributions to the world of metaphysics was the insight that both kinds of statements have equal force from the same source: pure human reason.
Since no external lawgiver is necessary to make 7 + 5 equal to 12, similarly, no external lawgiver is necessary for the synthetic a priori moral propositions that we also derive from human reason, acting alone.
4. To the extent it is cognizable, Premise A is internally contradictory. In addition to showing us that human beings can derive objectively real truths through reason alone, Kant also shows us that the AfM — in which individuals merely apply moral principles previously dictated by God — actually renders the resulting moral will subjective rather than objective.
Thus, Kant demonstratres in the Groundwork that the application of preexisting substrata renders morality contingent, rather than objective:

Kant 4:
Everything in nature works according to laws. Rational beings alone have the faculty of acting according to the conception of laws, that is according to principles, i.e., have a will. Since the deduction of actions from principles requires reason, the will is nothing but practical reason. If reason infallibly determines the will, then the actions of such a being which are recognized as objectively necessary are subjectively necessary also, i.e., the will is a faculty to choose that only which reason independent of inclination recognizes as practically necessary, i.e., as good. But if reason of itself does not sufficiently determine the will, if the latter is subject also to subjective conditions (particular impulses) which do not always coincide with the objective conditions; in a word, if the will does not in itself completely accord with reason (which is actually the case with men), then the actions which objectively are recognized as necessary are subjectively contingent, and the determination of such a will according to objective laws is obligation, that is to say, the relation of the objective laws to a will that is not thoroughly good is conceived as the determination of the will of a rational being by principles of reason, but which the will from its nature does not of necessity follow.

Thus: if morality is just applying the laws God independently set forth, then our reason becomes subjectively contingent; i.e., non-objective. As Kant says, “if reason of itself does not sufficiently determine the will.. then the actions which objectively are recognized as necessary are subjectively contingent,” and hence, morality would not flow of necessity from human existence. The AfM is self-defeating.
These four arguments show that we now have good reasons to reject both the fundamental axiom and the first premise of the AfM. Not only is there no good reason to suppose that objective morality exists, but even if there were, we wouldn't need to posit some objective lawgiver to explain its existence.
But the second premise of the AfM is false, too:
5. Premise B is empirically false. On face, Premise B seems intuitively true, even trivial — for a yardstick to be “objective,” the stick itself must not change from object to object being measured. So too, proponents reason, must there be a Single Universal Absolute Truth in order to judge different propositions.
Think about it more closely, however, and you'll see that this intuitive move is contrary to our everyday experience. For example: a medical textbook will display a “textbook” human body against which the doctor can measure diseases; the textbook will show what an ideal liver looks like, an ideal heart, an ideal brain, etc., etc. No single person has to exist with all — or even any — of these characteristics in order for us to diagnose a diseased liver. We know what an ideal liver looks like from looking at millions of human livers, even though no individual liver is perfect.
Similarly, we can develop an ideal, absolute moral yardstick from our collective lifetimes of reviewing human behaviors, even though no perfect human exists to serve as the embodiment of that yardstick.
To put it most simply: intersubjectivity is a valid basis for adjudicating judgments. Our experience tells us that you can produce invariant, objective standards from an aggregation of numerous subjective a posteriori sources. When you go to the doctor, he doesn't say, “Well, what counts as a healthy liver depends upon the circumstances.” No; he says, “This is an idealized conception of what a healthy liver should look like,” and then uses that absolute yardstick as a touchstone for ascertaining where your particular liver diverges from the good.
Every liver deviates from the ideal liver in some way; some more than others. Thus, no one liver is ideal to use as a yardstick. But from the intersubjective comparison of lots of livers, we can come up with an idealized liver to use when evaluating individual livers on a case-by-case basis.
Similarly, every human being's moral behavior deviates from the ideal of morality in some way; some more than others. Thus, no one human being is ideal to use as a yardstick. But, from the intersubjective comparison of lots of humans, we can come up with an idealized moral code to use when evaluating human behavior on a case-by-case basis and that's all we need to do in order to condemn the Holocaust. No “perfect morality” need exist just as no “perfect liver” need exist.
In a way, this is the antithesis of the ontological argument; one empirically valid method for deriving perfection is the aggregation of non-perfect things to develop an ideal from which those individual deviations can be measured.
Now, these five arguments have set forth numerous sufficient alternatives to explain the basis of human conscience — intuitionism, situational ethics, Kantianism, and now intersubjectivity. It should be clear that the AfM's eliminative inference is not justified.
6. An “External Referent” Need Not Be A “Lawgiver”. In your formulation, I notice that instead of “external referent,” you supplant Premise A with a much more narrow requirement that morals not only require something external but an external lawgiver.
But an external referent capable of making a yardstick consistent from person to person need not be the source of that measuring device. For example, a meter is defined by the International Bureau of Weights and Measures as the distance travelled by light in absolute vacuum in 1/299,792,458 of a second; prior to that, it was defined by reference to a platinum-iridium bar kept at 0 degrees Celsius. In order for a meter to be constant from measured item to measured item, a separate thing must exist that is invariant of the two items. That's all. Meters are not “made” or ordained by light or platinum-iridium.
Thus, at most, all the AfM would prove is that some non-human observer exists. It doesn't prove that the external referent is the source (or “divine will”) of the moral law. And remember the burden under the AfM; one has to show that no other moral system is conceivable.
These six arguments now cover virtually every contingency. I've shown that there's no basis for the assertion that objective morality must exist. If you don't accept that, I've shown that the assertion is undefined. If you don't accept that, I've shown that the assertion doesn't require any external referent but can be derived from human reason alone, in two ways. And now, even if you don't accept that, I've shown that the external referent need not be a lawgiver but can be merely a non-human observer.
Given the utter failure of the logical structure of the AfM, the next two arguments (7) and (8) provide two independent reasons to reject the principles behind AfM as well.
7. Inter-Christian disagreements over basic moral questions illustrate that absolute morality cannot practically exist, because even if absolute truths had an independent moral existence, they would still have to be filtered through the same human rationality that's available to non-Christians.
Even if one accepts the axiom that there is an external absolute, objective morality that governs human behavior, the AfM is silent as to how a nonabsolute, subjective individual is supposed to access that absolute moral standard. even if we presuppose that the moral law is given by God as revealed in the Bible, that really means that the law is given by what we think God wants as revealed in the Bible as we interpret it, filtered by our own rationality.
This is a pretty straightforward argument; it says that even if there are objective moral laws out there somewhere, we can't access those laws through anything except human reason. Thus, the most a human being can say is, “I'm pretty sure God's laws exist, and I'm pretty sure this is what they are.”
The problems are two-fold. First, the AfM is self-contradictory, because theists contradict themselves on basic moral principles. Suppose a homosexual and wants to know whether or not he should be “reeducated” in such a way as to renounce his homosexuality (e.g., through something like Project Exodus International). Now, some large number of people can quote Scripture and tell that person why God definitely, absolutely thinks homosexuals are an abomination and therefore why the individual should go through extreme measures to change his homosexual behavior. But a similarly large number of people, citing the exact same set of Scripture, will tell him to do the exact opposite!
On the other hand, there is really no secular arguments that I know of for why homosexuality is bad, and no secular reasons for a person to torture himself to stop practicing consensual homosexual behavior. So, this is another turn. if you're looking for absolute morality on the question of homosexuality, then Biblical morality is less helpful to you than secular morality.
And the same is true for many other ethical issues. At worst — on say, progressive taxation or the Kyoto treaty or whatever — the secularists are just as divided as Christians. But at best — on interracial dating and marriage, on homosexuality, on equality and the role of women, on the use of contraceptives to stop the spread of AIDS in Africa, on embryonic stem cell research, and so on — secular morality gives you a relatively unanimous, relatively clear answer whereas disputes within Christianity gives you a muddle.
Second, when we explore why different theists come to different answers on fundamental moral questions, we realize that the criterion theists use to differentiate between different theistic propositions is one of secular human reason! The way in which we authenticate revelation — i.e., how we determine that Charles Manson or Andrea Yates have not really “spoken” to God — is through reason. Thus, even theists concede that ordinary human reason is lexically prior to divine revelation.
Of course, each person fervently believes that his subjective reading of Scripture is correct and that all other readings are wrong. But — and this is the critical part — that justification is made not by reference to divine intervention, but solely by the application of the Christian's own rational processes. In other words, when someone says that his reading of a particular verse of Scripture is incorrect, he doesn't say, “I know I'm right because God told me,” he says, “I know I'm right because I have more rigorously and more intelligently analyzed Scripture.” This methodology shows that the whole AfM collapses like a house of cards. If human rationality is the filter through which absolute morality is processed, then we're all implicitly conceding that a non-Christian moral schema — which draws directly from human reason, acting alone — is superior to a theistic one. And that seems contradictory, to say the least.
In any event, if rigorous analysis, logical thought, and ordinary human intelligence is sufficient to evaluate whether God wills X or not-X, then it is also sufficient to evaluate whether X is good in the first place. It is no longer necessary to invent a God to have decreed X (or not-X), since you evaluate between X and not-X by reason alone anyway.
In short: internecine Christian disagreements — from political issues such as capital punishment, abortion, homosexuality, interracial marriage, birth control, and so on — to spiritual issues such as salvation by faith alone (or by good works), the existence and nature of the Trinity, the existence and nature of Hell, and so on, demonstrate conclusively that even if absolute morality existed in some external referent (e.g., God), there would still be no reliable way to know that the true moral law had accurately communicated to you or that you had divined it correctly from studying Scripture.
8. Finally, The Euthyphro Dilemma stands as a strong independent objection to the AfM. Plato, pretending to be Socrates, succinctly articulated the conceptual problem with this argument about 2500 years ago in the Euthyphro: is an action “moral” simply because God commands it, or does God command it because it is independently moral?
Instantly, you see the problem. If you select the first option, then morality is arbitrary, based merely upon god's whim. Had God decreed that murder, rape, torture, and genocide were moral, then we would be obligated to behave in that fashion and Hitler would have been the paragon of virtue.
More broadly, such a view of morality renders the statement “God is good” tautological, because “good” is simply another word for “whatever God does.” Worse, we are left with a sole warrant for all moral behavior — that we are to do or not do something based on whether God has commanded or forbidden it. Thus, we cannot adjudicate how to weigh moral principles in conflict because we cannot claim that one moral obligation is superior to another.
For example (following Wittgenstein and Nagel's criticisms of Kant), if I am harboring Jews in my attic and the Gestapo show up at my door asking if I am harboring any Jews, I need to prioritize the moral principle of telling the truth versus the moral principle of not handing innocents over to be tortured and killed. If I have an independent basis for morality rooted in my reason, then I can weigh one principle over another. But if you are a Christian who holds that something is wrong merely and solely because God commanded it, then you have no basis to say that one act of divine disobedience is better or worse than another. And thus morality becomes meaningless.
To be clear: the argument is not that God's decrees are bad because they can, could, or would change. The argument is that even if God's will never changes, it's still arbitrary. There are then at least three impacts as to why arbitrariness is bad when it comes to evaluating moral schema:
a. Arbitrariness is bad because it contradicts the premise underlying the AfM in the first place; that is, that there is some framework by which we can say Hitler is bad. But we can only say Hitler is bad because God happened to decree that genocide was evil in this universe by fiat. Had God decided that genocide was good, then Hitler would be a saint. So again, we see an internal contradiction: the AfM is less able to produce what the AfM says it produces — a basis to decry Hitler.
b. Arbitrariness is bad because it's tautological. Saying “God is good” then becomes the equivalent of saying “this triangle has three sides,” which, although true, is only an analytical proposition and thus is of no veridical content.
c. Finally, arbitrariness is bad because it assigns all moral propositions the same intrinsic weight because those propositions are only valuable because God says so. Then, I tell you that kind of equivocal value is bad, because it doesn't let you resolve real-world dilemmas.
On the other hand, if you select the second option and hold that there are independent moral goods that exist regardless of what God commands, then while you avoid the harms of arbitrariness, you also concede that the AfM is false in the first place. All the response to the AfM need show is that morality is possible without God; the phrase “God is good” then, ironically enough, becomes sufficient proof of that.
I apologize for the length but hopefully this clears things up.