I've only ever had instruction from "don't deliberately mess with stuff like breath" teachers. However, you seem to be finding Ajahn Thanissaro's approach useful, and he certainly talks about optimising the breath.
In my view, the sensible thing is to follow the instructions a teacher (or a selection of reasonably compatible teachers) and not worry too much about what the others say. Different teachers give different instructions, particularly when getting students started, that can seem quite contradictory. It doesn't mean any of it is wrong. They all teach what they found by experience to be useful to them and their particular students.
With more experience it becomes easier to see the commonalities, and/or why there are differences (e.g. whether they are putting more emphasis on concentration or on insight).
And keep in mind that your needs may change. One of the useful bits of advice I got from a moderately famous monk a few years ago was "If what you are doing seems to be working, keep doing it. If not, you might consider changing it."
Sorry for going a bit off topic, but I think that it is important to not get stuck in worrying about which method is "correct" and which is "wrong".