However, just by studying the early church fathers and their writings (and they wrote A LOT) in just the first 3 centuries, it is easy to determine exactly what sound doctrine is, where and when heretical doctrine came in; and who was the culprit.
So the bible is infallible because you decided it is infallible by deciding which writings passed around the first few centuries of Christianity you want to believe represent some form of orthodoxy - in spite of evidence to the contrary over such an orthodoxy existing (date for Easter, when Christ was scheduled to return, the lack of even factual agreement in the gospels, extent of Judaism acceptable being huge issue etc etc). That much of those writings didn't get included in the canon, that some of them seem to be very blatant forgeries well.. If it works for you, great, but you can't call out those who point out the circular logic going on there.
Would suggest fact checking the claim that you make about re-creating the NT from quotations. It just ain't so. And the half (?) which can be re-created doesn't really help too much if the counter-argument is early C2nd forgeries seem to be present and included in the canon.
Will have a read of your evangelical doctor by correspondence's book if it's about in my university library. The conclusion given to it on the Amazon view doesn't really fill me with great expectations of it disagreeing with the religion he joined aged 12. So fortuitous when that happens for theology students.