You have the right idea, but I would have used wider strips, at least 3/4 inches. The first thing I would have done before cutting is mark each piece with marker which does not fade (I used a ball point pen) where the cut would be. The next step before cutting is make a narrow zig-zag stitch just inside the marked line. This will get rid of most of the raveling and will make your seam more stable. I also would zig-zag the seams, again more stabililty. I've done this with crazy patch pillows. Believe me it works. It also works with napped wool and other fabrics that tend to ravel.