Joss.... I can't imagine the pain of living with his ongoing affair for 5 years. I want to tell you right now that you absolutely did the right thing by booting him out.
You can see that he is struggling with the reality now...something he never had to do before, while he was having his cake and eating it too.
You have been the rock, keeping things together at home and facing the challenges of raising an autistic child along with your other two. He is the weak one who had to go outside the marriage for excitement when the going got tough.
Take advantage of this time to find yourself again. I get the feeling that your H has beat you down with his criticism of you. Know that his affair had nothing to do with your"flaws" and everything to do with his weaknesses.
Now...IF you think you want him back, you can give him a roadmap of how to get there. But don't sell yourself short. If he really wants back, he will do the work. So far it sounds like you're getting words but no actions.
And you know what? You don't have to take him back if you don't want to. Yes, this has elements of MLC. But continuing the affair for FIVE YEARS while he knew that you knew and were hurt by it? That reflects a certain underlying lack of character.
Take a close look at who your H really was before the affair. You may be surprised at what you see.
What I've learned (after my ex's affair, a successful DB reconciliation, his MLC a few years later and our ultimate divorce) is that my ex always had narcissistic traits that I accommodated and didn't recognize.
You are under no obligation to reconcile unless YOU think it is the best thing for YOU.
Also...a word about the kids. I understand doing everything you can to save the marriage for the kids sake....that's certainly what I did. But don't assume your kids would be happier if you reconciled now. My ex and I never separated when he had the affair, but I learned later that the kids were very anxious during those next few (good) years, they were waiting for the other shoe to drop. So now that you and H have separated, don't assume that the kids would be better off if you reconciled.
The very best thing you can do for your kids is to model strength, optimism, moving forward. My kids definitely benefited from my example of resilience, it helped them feel like they could survive it too.