I looked at the photos yet again. If you can get it blocked, and spray starched, you could probably just machine quilt big X's through the squares and maybe do a zigzag in the outside border. (You could also add zigzags to the sashings, either inside the lines you already quilted or crossing over them.) This would be a lot less work than undoing all the quilting, especially since you already have the binding on.
The key here would be blocking it, which would mean stretching it out and getting it flat allover. The spray starch would help stabilize the top and backing so they don't stretch while you are adding the additional quilting lines.
The zigzag would be straight lines; you just have to stop at each point and turn the quilt. This is still pretty easy to do with a walking foot.
Here's a tutorial on how to block a quilt:
http://www.dreamweavers-quilts.com/q...hort-tutorial/