I'm confused. Closed is closed. Unless she intends to change something--leave the existing relationship, talk with her partners about opening up--she has told you that she doesn't intend to move forward with a relationship with you. Also, the health of her triad relationship, while it may appear unhealthy to you, is ultimately not under your control. If she chooses to stay in it, you have to control over that.
I don't know. What you're describing sounds like a recipe for a lot of drama.