I would like input from others on what I am going to tell you because I feel I am going to be a little bit harsh. I want to apologize in advance but I am quite worried by what you described.
First: The total lack of affection or gestures of affection is really something alarming, it's raising a BIG red flag on his motivations why he is with you right now. You need to dig on that question. Having difficulties being with intimacy while piecing is somehow common for some but a total lack of affection is the sign of something really serious.
Second: Also, his ambivalence/reticence/refusal to let go his very borderline flirty behavior/relationship with women is really troubling, it sends the message (at least from my perspective) that he is not ready at all to change that very bad habit and he doesn't care about YOU. Do you think he might be "craving" that kind of attention from them to feed some "narcissist" needs. Please read about what are the personality traits of a narcissist and how they manipulate back and forth people to stay in control/power, and see if it applies to him or not. I don't want to imply that he has one but it looks like one.
Third: His passive aggressive behavior in regard of your offer to pay for MC suggests he doesn't want at all to get one, because he doesn't want to have to reflect on his actions in front of someone who will be listening to your side of the story too. So the best for him is to avoid it at all cost, because somehow he knows he might end to look like a villain, which he is: a guy who cheated on his wife and who is still somehow blaming her for it, while not really putting any effort to change his own behavior. That's not good for his image and it doesn't want YOU to gain the upper hand which goes against his own interest, he wants you to keep waiting while refraining yourself to ask any questions or come up with demands, now the question is WHY?
The program he has been following about "working on himself", fits his needs because it's a one way self analysis without the input of someone.
Fourth: his rhetoric about wearing his wedding ring (+ you buying a new one for him) while not having any gesture of affection or being considerate of your triggers smells highly suspicious/plain manipulation. I applaud the answer you gave him.
In my opinion, right now he is not piecing with you, he is up to something.
Now my last question is a tough one: men usually don't leave until they have a plan B, they keep going with what is convenient for the moment until that plan B is set up and ready to go. Do you think he might be stringing you along because of whatever reason?
I am very sorry for all the 4"X4" I wrote. Knowledge is power. Also, read again the article about pursuer and pursuit...
Me 52+ WH 57+ Married 20 + Piecing since 2016 (ready to give up...)