Bear, I think you've tried really hard and done all you can at this stage. Rather than focus on what you want from him, think about your future and what you want.
Please don't take offence, and I was guilty of this too - but would you say that perhaps you mother him? If he is used to you always taking control and running things, then he will gladly sit back and allow you to become a mother figure. This could, perhaps, explain why he had the affair? He didn't see you as a partner, he saw you as a mother figure, just a thought.
Anyway, I really would advise you to bite the bullet and tell him you want him to leave (for a set period of time) whilst you decide what you want. You need this time alone to evaluate fully what has happened, and to see how you feel when he's not around. Crucially, he needs to find out what he could lose. As you say he has no empathy - you need to force the issue. At the moment, he's still at home, jumping through the right hoops and saying the right things - the things you want to hear. But he's not taking the initiative, may be because he's quite comfortable with things. Men are often lazy, and will go along with the flow for a quiet life. But he needs to find out exactly what it would mean if you were to permanently split - so give him a taste of this. It will take guts, but it might be the wake-up call he needs - he will have to think for himself, fend for himself, and cope with his emotions. He will then, if it's meant to be, do all he can to win you back. He has to appreciate you - and right now he doesn't have to - because apart from counselling, etc., nothing has really rocked his world.
If you do this, tell him that it's strictly no contact except regarding the kids, and he can see the children frequently.
In other words, let him miss you. Give him a reality check. Otherwise, I think you'll just go round and round in circles. Also, he needs to value your emotions/hurt and feelings - let him know it's not just about him.
Good luck - you sound very strong; you'll get through this. But try as hard as you can, you can't change someone, only they can change themselves.