Caleb, I think I understand the thrust of your argument, but tell me if my recollection of it is a false caricature:
1. In order to understand that God is sovereign over everything, such as reason, our existence, morals, etc., we must reason to that.
2. But if we have to reason to that, then we are using reason in a "neutral" or autonomous fashion; that is, we cannot presuppose that God is necessary for reason's existence before we complete the AFR.
3. .: insofar as presuppositionalism affirms that God must be presupposed at the beginning of all argumentation (including the AFR), presuppositionalism is a faulty method.
Correct me if that is not representative of your argument.
I struggled with this as well, with my problem manifesting itself more so in the fact that I could not avoid the "piecemeal" method, which is present in your method too, seeing as you said that the AFR and the teleological argument cannot prove the existence of the Christian God. The solution that I found seemed to sacrifice the certainty of TAG in rationalistic terms, changing it to certainty in Scriptural terms. Let me explain:
As your argument points out, in the AFR we cannot avoid but
not to grant God's existence at the beginning of the argument, for the maintaining of intellectual fairness. Therefore, if we are to accept God at the beginning of the argument, it would not be for rational reasons, but for some other reasons. I termed this type of commitment as one to a
pre-rational authority.
And what reasons do we accept God as authoritative prior to the AFR? Because we simply know that we ought to do so; it is implanted within us as a
sensus divinitatus. I think that the doctrine of our sense of deity is the result of a faithful exegesis of Romans 1 as well as an appeal to experience: if we did not have God as a pre-rational starting point (i.e. if we did not have a sense of deity which promoted that we accept God prior to our reasoning processes), then no one could help but remain a non-Christian. If there were no sense of a deity which the Holy Spirit coerced us to embrace as Father, then autonomous reasoning would be rampant across mankind, and with it autonomous philosophies, which lead to the destruction of knowledge as Van Til and other Reformed philosophers have shown. Thus, Christianity/Jehovah is ultimately selected by a pre-rational submission to Scripture, prompted by our regeneration and
sensus divinitatus.
This helps to avoid the problem of necessary autonomous reasoning, where even TAG would seem only to prove a "piece" of Christianity, and this is what ultimately differentiates presuppositionalism from evidentialism. This demonstrates that we are
not required to start with an autonomous basis and that it is perfectly alright to accept the entirety of Christianity as a rational belief without having to build an impermeable apologetic (of which many believers are incapable).
Of course, you might object that this sounds fideistic, which is where the apologetics come in. I would use TAG to demonstrate the absurd inconsistencies of competing philosophies, evincing that without accepting God, nothing makes sense. I need not rationally
prove that God is an essential pre-rational authority, but I can rationally prove that every competing system thrown my way is self-destructive and sinful, giving extremely compelling rational reasons to believe in Christianity.
In a word, the sense of deity (and witness of the Holy Spirit) is the
proof of Christianity and TAG is the
persuasion. (This is what I meant when I said that I sacrificed rationalistic certainty for Scriptural certainty; we don't prove God 100% with a rational proof but rather with our sense of deity). Even if we failed in our arguments, Romans 1 would not cease to be truthful; e.g. even with our faulty argument against the philosophical consistency of materialistic atheism, the atheist would stand condemned before God, suppressing his knowledge of God.
I apologize for the length.
Ben