I think I would do either allover diagonal lines or cross hatches, with a decorative stitch on my machine. Anything with an open swirly or wavy pattern to it (lengthen the stitch length of the pattern) would contrast nicely with the geometry of the piecing, and add a lot of interest. I would measure and carefully place pieces of blue painter's tape onto the top, and decorative stitch alongside the edge of the tape to stay straight. Pieces of tape can be repositioned and reused several times. Just be careful not to stitch into the tape. Very pretty quilt, by the way!