Barb,
Sounds like you have a wonderful idea.
If you want it to look like reverse applique, you can take a piece of black fabric, cut each piece out and fuse it in place on the black fabric, then take the sewing machine and clear thread and do the pin stitch around each piece. This is much quicker than doing the bias stripes and it looks really good. You will need to make a pattern from your picture, then make cutting template for each piece and a placement template.