I agree with everyone who has suggested a continuous line diagonally through all the blue squares, in both directions. Yes, it's hard to go through all those intersections but by modifying your stitch to a "punch & stab" just at those places you can succeed.
For the white rectangles, rather than use tape laid next to the seam take a small piece of that tape and put it on the thumbnail of the "non-needle" hand & use that as a 1/4" guide for your needle to aim for. Another possibility--I think an elongated pointed oval in each one would be pretty. There is also the "egg & dart" pattern that would work beautifully.