I mean, is it possible? Crisis/trauma can spur major growth, like Alison said earlier-- but will that happen for *him*?
The ONLY way your H will do the kind of internal work you're talking about is if CONSEQUENCES are imposed for his bad behaviour. That's why I keep harping on about the importance of YOU being the one to leave if you want any chance of reconciliation. He won't change unless he feels enough pain and shame to do so, and even then he might turn and run for the rest of his life - that's the risk you have to be willing to take. You have to leave him and be willing to lose him forever as a result. On his part - he will never value something he has never had to earn. On your part - unconditional love does not mean being an enabler.
The consequences must be severe. He completely loses any access to you. He loses 50% access to the kids. He is exposed as an adulterer to family and friends. He gives you and the kids long-term financial support. This is not done out of anger or to punish your H. In fact, it's the opposite. I think you are doing an unkindness to him by refusing to leave. I think you are standing in the way of his personal growth by refusing to impose consequences. Change is hard and people like to be comfortable. He is too weak to do it himself. Leaving him could be the impetus for him to finally change. Leaving him could be your greatest act of love.
Sidenote to Alison - DB has its uses, but it lacks a lot of nuance when it comes to abusive relationships. I believe infidelity is inherently abusive and therefore feel like I'm the black sheep of DB with my 2x4s coming from that angle. I followed some absolutely terrible advice in the five months between BD and filing for separation - I'm still shaking my fist at Laura Doyle. But it was all honest and earnest and part of the journey. I do believe everyone gets where they need to be eventually, with or without the 2x4s. You are in a fantastic place now
ETA: May, you are also doing great! I know you will get there on your terms and how important it is for you to own that.