I like the idea of quilting along the edges of the boxes inside the print areas. Definitely don't try to quilt less than what the batting package calls for...that way lies disaster.
My only other thought is trying to come up with a quilting pattern in the sashing areas that might look like a chain link fence...diagonal cross hatching with a bit of a wiggle? Definitely do a test sandwich, or three. Try different threads, different patterns, anything you can think of. Then bind it (them), and wash and dry several times. Much will be learned!