Obviously he wants his cake and to eat it too. He is deep in the fog and I think there is nothing you can do at this point to bring him out. If divorce papers weren't enough then I doubt anything will help.
Take care of yourself and put your needs and yourself first. Obviously he can't tell you the truth now. You will be able to tell he is lying because his lips will be moving. Someone said that to me of my WS before he swore not to lie again. Which I am taking with a grain of salt till I see proof that he is telling the truth and even then I will still be suspect.
If he is not in NC with her, if he is continuing then you have every right to write him off. You don't need to deal with his needy, selfish, lying self.
Remember you are among friends who get what you are going through. Only a BS can truly get the pain we are in. Circumstances may be different for all of us, but the betrayal is the same.