Don't use Starsky's words, they will backfire, because she doesnt want to work on it.
Sometimes we (understandably so) get so focused on how we should or shouldn't or can or can't have a relationship, that we don't focus our time on having one.
When you walk away when she's still crying, she's going to turn to someone else. When you are talking about the relationship, you're not necessarily having one.
So just start a relationship with her. Have fun. Fun leads to more love. Do some nice things together. Just be with her with her drama and stay through it. It might not feel good to you to do that. What I read through this is that's what she needs and wants.
Distancing is not going to help you with her. Of course clinging won't either. But really being there for her/with her will. Lightening up the situation will help too.