Theoretically, I guess your batting could migrate from one end of the quilt to the other along the quilting lines. Realistically, I doubt that would happen. However, you would still be better off (and it would take less time) to do some other type of quilting that went in both directions. For this type of quilt, a meander would be fine, or swirls, or ... whatever you like. If you don't enjoy free motion, perhaps you could SID for every 3rd seam and make diagonal lines every 6 inches, following the direction of the joins in your strips if you joined them on the diagonal, or straight up and down if you joined them at right angles.