Continuing to LG:
For reasons such as these it would be advisable to make a further distinction, not just between "small-t tradition" and "Large-T Tradition," but also between "Deep Large-T Tradition" and "Shallow Large-T Tradition."

As for your "I don't believe Jesus could err," etc., right, given the faith in Jesus such as the Christian church professes, so that allowing that the Jesus of faith could err would be a kind of contradiction in terms. By contrast, the historical Jesus most certainly could err, and seems to have done so on at least one important matter, viz. the apocalyptic timetable. And it is that fallible Jesus who provided the data from which a small number of first-century Christians constructed their respective portraits, without themselves necessarily understanding all the implications of their work. And we should note that the Holy Spirit did not demand uniformity, but allowed for such limited understanding to be the seed of much subsequent fruitful discourse.