I'm confused over how the backing can be too big. Maybe you mean the top is too big and now you don't have enough backing?
I would think the Amish would tie or baste a quilt by starting in the middle--not the bottom--unless they load it on a frame first. I have done that myself when I wanted to tie a quilt but didn't want to crawl around on the floor to do it. It's a little hard on the back to stoop over the frame and tie a quilt but not as hard crawling around on the floor.