I'm not sure from your post if he is polyamorous or just polysexual.
Either way, while I can relate to his feeling trapped when you didn't want to open the relationship, I don't condone the cheating.
Regardless, it seems to me that the situation for you is that he is not going to stop seeing other women. He hasn't been able to, and I doubt he is going to start. If you want to stay with him rather than break up, then I guess opening the relationship so that you know what he's doing, who he's doing it with, and you place your own terms and boundaries, etc... that could help.
But if what he likes is the thrill of cheating, he'll break your boundaries anyways.
Marriage counselling sounds like an option if you want to find an outlet that both of you can live with. If it ends up with him doing whatever he wants and you resigning yourself to letting him, I don't see you being happy that way, and I'm not sure how it's different from cheating except he's also rubbing your nose in it.