A friend was trying to take off a binding to put on a new one. The old one needed replacing. She was working on taking the binding off when I said, "Why don't you just cut it off?" In about two seconds, she had her ruler and cutter out and in about five minutes the old binding was GONE. Then it was easy to put on new binding.
You would lose points with this method - if there were points on the edge - but it sure is fast and easy. With an old quilt, you may not care any more about losing points or not.