I would either have proof that he is being honest and really does want to change or proof that he is still lying and is not worth my time and energy trying to save a marriage that is hopeless
This is really quite a simple matter.
Just tell him to give you his phone and that he can un-delete all those texts IN FRONT OF YOU and show them to you himself.
If he doesn't know how to undelete them, keep his phone, and go with him to the nearest phone service store and have him pay them to undelete them in front of you.
And, that, if he refuses, you are calling a lawyer tomorrow and you are going to FILE, with no possibility that you will ever change your mind.
If he wants to save his marriage, he will comply.
If he doesn't comply, then you have your answer.