J, the problem is that in answering your questions about the nature of the calls, he may lie to you if he's covering up the continuation of the A, or he may lie to you if he's having a problem ending the A on account of his inability to do so at this time, and so on. Like you say, "who knows?". It could be anything.
During our convo about trying for a couple months and evaluating things after the first month
That's a rather short time limit. Don't put time limits on these matters. They are not on anyone's time schedule.
but can you understand why I'm really having trouble with that? He lied.
Sure, anybody would be upset over that situation. I wouldn't call his breaking a promise to not call the OW a "lie". We don't know why he's contacting the OW after he promised not to.
How am I supposed to rebuild our M and the trust that goes along with it when there's still this wall of secrecy obstructing my view?
Darling, not all marriages get salvaged. You must always consider that it may not work out.
And if I do ask H if any contact has been made by OW or himself without bringing up my evidence, and he were to say "no, not at all", then what? How do I handle that? I know I won't lash out and accuse him of lying (although he would be lying).
It sure looks like you're not going to solve this thing by asking questions. Instead, you have to take a giant step back and again be the person you became and do the things you were doing that worked to have him turn around. I'm guessing that things moved a little too quick and he either lapsed back into the A due to the reassurance he had from you that he wasn't losing you, or he's not sure where he wants to lay his head, or the OW owes him money and he's been trying to collect... who knows, right?
No more ILY's back to him. You know what to do. And this time, pull away further.