Is there a third way out from having to choose between partners who want monogamy & partners who don't?

My wife and I are poly. She has a boyfriend, and I have a girlfriend. Neither the boyfriend, nor the girlfriend are involved in other relationships. They both want more. In fact, they both want to have monogamous relationships, but all of us will be sad if there are breakups. So, aside from either the girlfriend/boyfriend breaking up with us, or the girlfriend/boyfriend being "stuck" in a poly relationship, is there some sort of third option?

No, there is no third option. There will be sadness if breakups have to happen, but there will also be sadness if people are "stuck" in relationships that don't make them happy. There's a choice here that needs to be made, and there's no way out of having to make that choice. Life is full of tough choices, and each path we pursue comes at a cost. It's painful, but it's just part of being a human who has relationships.