Have you thought about making the black strip as an applique? You would have to iron under the edges or sew it and turn it inside out. Ironed down edge applique would be simpler. Then either hand stitch it on or topstitch the strip to the original top. Accuracy would be the key. You would not have to rip anything out if you did it this way. Or, you could use steam-a-seam lite and make it a raw edge applique and satin or blanket stitch around the black strip.
As with anything, there isn't just one way to solve a problem. It's whatever works best for you.
Happy quilting,
Barb