You're correct in thinking IC would be helpful for him... HOWEVER... he's still working directly with one of his AP's and is still in contact with the other. He is not a candidate for R right now.
I think your MC right now should not be focused on intimacy with each other or mending your relationship. He's not interested in it. He's still actively in his A's - especially if he's doing overnight travel with his one AP. There's no way that it is not still physical if they're out of town together and staying in the same hotel. Or even different hotels. It's the easiest situation for them to sleep together. You don't have an M to take to MC right now. He's checked out. He's still actively cheating.
I would continue MC in the sense that you focus on your communication skills. How to argue constructively, express yourselves without attacking, and discussing the "business side" of the M. Things like childrearing, money and maintaining the house should be your only communication right now. There's no M emotionally. Communicating your hurt to him is futile. He's still actively in his A's.
Frankly, I think that he's not interested in continuing the M. Really, I would focus on a legal S or a D solution right now. Continuing to try and pursue R with him is pointless while he's still in his A's.
Continuing MC for communication purposes is only one reason to continue. Getting WH in for MC can be a shallow entry point for him to get comfortable with counseling. Once comfortable, he could choose to pursue IC. Thing is, HE has to want it. Just like HE wanted and entered his A's.
From what I remember of your story, he blames you for his A's because you cheated first. Blaming you for his A's is BULL SHIT. He could have D'd you, he could have S. He could have decided to stick it out and R since you're doing the work. LTA's are tricky- 5yrs is a long time to be bonded to another man. It pretty much makes your WH rethink the entire relationship. He's not wrong to think that the entire M was a lie. Thing is, he's wrong to blame you for his cheating. Did you have a gun to his head? NOPE.
There's a poster on the wayward forum who initially saw herself as a WS, but came to understand she was the victim of severe emotional and physical abuse. Cheating is abuse, however, there are many situations where having a revenge A is a free choice. Yours was such a situation. Your WH was damaged before your decision to have an A. There was something lacking in his own integrity that permitted him to have his own A's instead of pursuing R, D or S.
I suggest that you pursue legal S or D since he's not actively working on himself. You can pause or stop the process at any time if real progress is made.
Also, he needs to inform his employer of the relationship with his AP. He needs to get off projects with her and go NC. They can communicate through their superiors if it is necessary for business purposes. That's the first step to even consider R.
Yes, you broke the vows first. However, you didn't pour a whole tanker truck of gasoline on the house fire. You're in IC, you're doing the work. You're becoming stronger. Sometimes it happens where the WS does so much work on themselves that they become the stronger spouse. Some use that strength to carry their BS through their own pain and into an R situation, or at least a cordial D if R is not possible. Your WH is doing none of that and isn't even done with his A's. He is not R material for YOU.
Do you want to be punished for your A for the rest of your life?
Do you want to live in a relationship devoid of respect and mutual care?
What do YOU want?