I believe that you have realized that the many suggestions to open the binding, add a new backing, rebind and tie is the way to go. I can't imagine trying to remove "all" of the black binding so my suggestion would be (and I am no quilting expert) to snip off the "already" ripped pieces, then follow the steps above. Because of the problem being with the "black", I would suggest that you tie from the back and at least a "hand" apart. Hopefully, this will stabilize the black fabric, which will no longer be compromised by use. There are many YouTube videos that show how to tie. I believe it is a double stitch process. The closer you tie the better. Good luck with hugs.