PL, there was a lot to digest in that post but I want to address your general question.
Quote: I have heard that nothing can move forward until the A has ended. But I have also heard that the A doesn't matter. How can both be true?
It can be true because the statements are about two different things. They apply differently.
The first, that nothing can move forward, IMHO, means that your R is likely to stay stuck at a certain point, usually the point where H is comfortable (no sex, very little affection) until the A is over. Until then, nothing, i.e., no relationship growth, can occur.
The second statement refers to YOU. The A doesn't mean anything to you. It's not being done to hurt you or to affect you in any way. Your paying attention to it is the only power it has over you. So, when you hear that the A doesn't matter, or that it's not the REAL issue at hand, what is really being said is to not put all your focus on the A because to do so means losing sight of two very important things. One, yourself, and two, that there are other, more important issues in your marriage that will have to be addressed.
The point of both statements is to get you to understand that the A is not your main problem, your marriage is and more than that, the only way to work on your marriage right now is to work on YOU.
