Yep, I thought of doing that for the backing too. Should be a WHOLE lot easier than trying to do it on the floor. Just drape the backing on the frame first and put the top over it to size it.
About the vacuuming... that was part of the inspiration of using the frame. If I was going to lay it on the floor I needed to vacuum first. I didn't want to do that right then but I wanted to get the border done.