I definitely think honestly would be for the best. I think you owe it to your partner not to go behind his back, and I hope he'll be fine with opening the relationship. Sadly I think you did break his trust on a number of occasions so he's likely to want to take it slow if he's willing to open up. But I certainly think it's a discussion that should probably happen.
Aside from that, I don't really have much advice, any advice would depend on his reaction to your conversation. I also suggest that whatever boundaries he puts in place, you follow them the best you can so you can prove to him that you deserve his trust, and maybe he'll be less strict as time goes by, as is often the case. But if you break his trust again, he probably won't want to hear about it after that and you'll have missed your chance.