Yes I thought you would say that you had indeed been trying to compete and become the perfect woman. I understand why people do this, but it is utterly pointless because the affair was never about you at all. It's also entirely the wrong approach, because it is so one-sided. There's a world of difference between a couple trying to make changes after an admitted affair and working from a clean, honest slate - and what you have been doing. It just serves to make you feel exhausted, as if you are not behaving naturally and comfortably in your own marriage and in your own home and most of all, it is utterly corrosive to try to compete with another woman. It must have also been horribly difficult for you knowing that they were still working together.
Instead, your H should have been wooing you again after what was a horrible betrayal, but although you don't say what happened between your threads, it doesn't sound as though he ever came clean and gave you the respect of honesty about his actions. Did you ever contact the OW? If the affair is still going on (likely in my view) then admittedly, if she denied it to you then I'd take that with a pinch of salt, but from what you've disclosed so far, the only version of events you've ever had was your H's. He lied to you when you found the first phone bills and only when he couldn't lie any longer, admitted to only what you could prove. He then changed his billing arrangements to permit further secrets.
What you need now more than anything is incontrovertible and independent information, because I wouldn't believe a word that's coming out of your H's mouth right now. There must have been a catalyst for this recent change of heart and I would start to find out whether the OW is now miraculously out of her "abusive" marriage.
Unfortunately, lots of women in abusive relationships don't seem to make the link that their new love interest is being abusive himself to his wife, because as long as he's not abusive to her it's somehow permissible
.
I really hope you can summon up all your strength and courage and tell him you have more dignity than to let him change his mind again.