I checked your archived material below, came up with clippings pasted below. I agree that a TA is deductively valid, or at the very least expressible as a valid deduction after it has occurred.
Circularity does indeed seem unavoidable.
Since a proof for LC involves using LC, I think we need to seek its authority in theology, and ultimately in revelation. Looks to me like your possibility 5 is the usual cliff off which the unbelieving mind is driven, sooner or later. I know what he was getting at, since a TA is certainly deductively valid. I wonder if he was referring to the fact that, since a TA deals with a transcendental of human experience, its conclusion is necessarily presupposed in making the argument and thus there is an element of unavoidable circularity which would normally be considered fallacious in a deductive argument. I wonder if we could begin a thread to discuss the ways in which TAs, in general, can be refuted.