This is sounding more and more like an issue with your girlfriend. If you have been open and honest (even more than you are comfortable with) and she still is not willing to have a relationship with you, then she may have trouble with trust. Some people have difficulty with trust even if the person they are with is trustworthy or has proven themselves trustworthy. A trust issue like this usually stems from a childhood abuse or dysfunction in the family.
One of the clues is that she continues to bring up your past, even though it has been talked about and you have dealt with it. That is a sign that she cannot accept the situation the way it is. She is pulling up something from her past that keeps her from accepting the truth.
Although you cannot make her do anything she does not want to, you might consider suggesting therapy. Your relationship seems very good on all levels so it is worth taking the time to work on this issue together.
Also, you can use self help to find ways to help your girlfriend see that she needs to work on her trust issues. Here are some resources to help you get started:
The Courage to Trust: A Guide to Building Deep and Lasting Relationships by Cynthia L. Wall and Sue Patton Thoele
Daring to Trust: Opening Ourselves to Real Love and Intimacy by David Richo
Broken Promises, Mended Hearts : Maintaining Trust in Love Relationships by Joel D. Block
You can find these books on Amazon.com or your local library may have them for you.