What if you just did straight diagonal stitching over the whole quilt....in one direction only....and that being perpendicular to the diagonal lines formed by the small 4-patches? If you did that, I think only between the 4-patches where they meet, not through them. The diagonal lines formed by the 4-patches and larger squares is so strong visually that quilting lines in the opposite direction would balance out the movement somewhat.
It IS a lovely quilt and you did a fantastic job on it!!! Karen