Actually, one of my most embarrassing moments was finding a quilt I absolutely loved at Road2CA. It was black with all different colors of thread-work making up the pattern. I found it and then lost it. Finally, as my daughter and I were searching, I found it again and showed it to her. She looked at me and said "Mother, that's the back of Sharon Schamber's quilt." Her applique quilt had won the $100K challenge. She had used the same thread on the front as on the back (different color for each applique color). It really looked gorgeous. You might use white on both top and bobbin. You could use a Sashiko design overall to quilt and you'd end up with a gorgeous look on the back.
Make another block of leftovers and quilt a small 12" sandwich. The white on the navy back might just be gorgeous.