oh goodness, you are having a time aren't you? I too stitch pieces together with what ever i have on hand. even black. I did a decorative stitch on a pillowcase i just made and had black in the bobbin and white on top. didn't show at all, whew!
yes i guess you could finish that block with black in the bobbin. then change to what ever you have on hand that blends in better with your backing fabric if you can. if not, white is fine.
good luck.