My first thought was to ask for a general slow down for EVERYONE- you and he, he and gf, you and bf, and anyone you're each seeing casually. And maybe you don't need to ask him and gf to slow down. Maybe slowing down things for yourself and explaining how you expect it to be helpful for you will be enough to get him on board with the idea of a general slow down all around. Because ultimately you can't dictate his relationship with her (not that I think you're trying to do that), you can only make relationship decisions for yourself. Just make sure that you communicate to everyone YOU'RE involved with what you've decided to do so they don't think you've disappeared or are ignoring/avoiding them!
ETA: And I definitely second everything nycindie and anne said.
Pan Female, Hinge in a V between my mono (straight) husband, Monochrome and my poly (pan) partner, ThatGuyInBlack