I'm glad to hear you have strict healthy boundaries about abuse.
I would give him some time, but not too much time, to hold up his promises. I wouldn't pressure him with a demanding tone, but ask. And continued discussions regularly about where the two of you are going and how you are going to get there. I think relationship maintenance and to make sure that there is forward momentum is crucial. No complacency, because that too easily leads to sliding back into old behaviors that weren't helpful to the relationship.
If it were me, I would tell him I'm sorry that he feels the shame and guilt over what he said that night, but that with time he can prove that he is a good guy. Simple wording, yes, but he will know what you mean. I would never promise someone that I was going to hide abusive behaviors. In fact the opposite, I would promise I was going to share them, and quickly.