He's still not choosing you. He didn't mention you once as a factor in his decision except to blame you yet again for 'damaging him'. Poor sad sausage.
Your own sadness is palpable in this update, even though you have ostensibly won the pick-me dance (for now, that is, until the next protest or birthday or whatever ridiculous reason for breaking no contact happens).
He wants to do the right thing by AP? What about the right thing by May. He owes it to the children? What about everything he owes you. What about respecting and honouring you enough as the mother of those children, as the wife he vowed to love forever, as a strong and beautiful woman who is deserving of love, to get down on his knees and THANK YOU for even giving him the option to choose?
Brutal honesty time. You are not a positive factor in his decision. You are something to be endured so he can pat himself on the back and tell himself how noble and self-sacrificing he is. "This is what's best for the AP and it's best for the children" - look at Gandhi over here! Everyone's getting what they want except H, so May will have to work harder than ever to prove he made the right choice. That's not exactly going to help with his sense of entitlement, is it?
I'm getting a little heated typing this out, so I'll end before I cuss out your H, and I do apologise if this comes on too strong. I do believe in love and I believe in reconciliation if the proper actions are taken on the cheater's behalf. It could still happen with you two. But not with this weak stream of hot garbage from your H.