LC my first port of call would be within the area of "incontrovertible evidence". I seem to have said this a lot in the past few days, but how does he get his phone bills? An old bill you've got lying around will allow you to register him for online billing and you will be able to see text use up to the point when you made your discovery - and up to 2 years worth before that. I assume you know OW's number, but no matter if you don't.
If that doesn't bear fruit, then talk to OW's H privately. Tell him that as far as you are concerned, you believe an affair was very much ongoing for your H when he left home.
Third, if your DP is saying he wants to come back, tell him you cannot trust what he has been telling you and the only way he can regain a smidgeon of belief is for him to turn over all his credit card and phone bills for the past few months. That you will look at these and get back to him. Now, that might make him finally tell you the truth, or if he's got nothing to hide, he will demonstrate his trustworthiness by becoming an open book, even about the past.
And even if he wants to come back, if it's only because OW belatedly had a touch of the seconds and chose her husband, then that is a matter for you in terms of what you can accept and forgive. I couldn't ever have done that, I will be honest.
And I think he is protecting the OW with these lies to you, as well as, or if not, himself.