You can use zippers. Look for separating sleeping bag zippers, you will need at least 2. With the zipper zipped, find and mark the center of both sides with a permanent marker. Sew one side of the zipper to the take up leader, matching the centers. Do the same with the backing leader.
Now you can machine baste the quilt backing to the zipper and just zip it on. You can also pin the backing to the zipper. Might be easier on your hands if it's not on the frame.