Welcome to the QB!
Another idea...if you aren't using batting or if you are using a batting that doesn't require close quilting, you could quilt some type of design such as a star in each of the squares. It would require a lot of starts and stops, but you would be avoiding the really thick seams, you wouldn't have to try to move the quilt as much as doing straight stitching all the way across the quilt (repeatedly) and it would look really cool on the back.
Good luck with whatever you decide!