So I tried cutting 6-1/2 inch stripes, trimming it them with the angle at the end of the binding tool, and sewing it to a 6-1/2 inch square. Then I used 3 pairs of colored strips instead of 4 pairs. It worked out perfectly. I added a one inch (finished) inner border and then a four inch (finished) pieced border made from the remaining 2-1/2 inch strips. It used 12 jelly roll strips in total.
I have no idea yet how to quilt it. If I went with an all-over quilting design, I don't know what color of thread to use, as black seems a bit harsh for the colored areas. Also, any one of the colors might look odd in the "other colored" patches. Oh, well, it can stay in the UFO pile for a while until I figure it out.