I think I would do parallel zig-zag lines matching the piecing, and extend them thru the borders. Go right thru the middle of the center zig-zag, then do parallel lines to both sides, maybe an inch apart, ignoring the seam lines in the piecing. THat is, don't try to stitch in the ditch, or hit the same spot in each chevron. It should be pretty easy to keep your spacing using the foot of your machine, or a quilting bar if you have it. Maybe draw marking lines across the quilt at the corners of the zig zag, so you'll know when to make the 90-degree turn.