If not, then I think you should set a very clear boundary.
The next time he talks about getting back together, I think that you should make it clear that this is his last chance. Tell him (and mean it) that if wants back in, he has to completely break off all contact with OW forever, or you will file for D. Tell him that you are not going to be jerked around like this anymore. Then ask him again if he really wants to move back in. If he says yes, he has to give you passcodes to voice mail and email and account for his time.
The LORD is near to all who call on him, to all who call on him in truth." (Psalm 145:18)