I have a 3rd option, which I think would be a little easier. It would be to use black thread, a walking foot, and a serpentine stitch down the middle of all the black sashing. The advantage of a serpentine stitch is that you can sew it very fast and not be overly concerned about staying exactly on the line (or in the middle); small variations don't show up in a serpentine. I am suggesting just one line down the middle because the sashing is narrow and it would cut the amount of sewing time in half (compared to doing the serpentine on top of each black seam).