Why did he double delete them if it's all innocent and only started Friday? He would want to show you, to prove nothing more has gone on.
He has suggested changing his email address and THEN giving you full access. Why? Why not full access to the email address he has now?
He is crying, trying extra hard because he is trying to make you believe hevisnt up to anything.
Look Op, I get you dont want to face this. But if you ket ut go, he will do it again but just be better at hiding it.
It's totally up to you what you do, but you either face up to it now. Or face up to it in a few years when you find out, again.
He isnt being honest. He has got rid of it all, which he wouldnt had it have been innocent. He is expecting you so be the good little wife, believe him, he wi be sorry for while and then go back to it.
If he believed you texting someone you really shoildnt have been, wouldnt you show him it was entirely innocent?
Personally, I believe by moving past this now, you are saving up trouble for yourself in the future.