I think what you are looking for is called sew and flip. This is also in the
book "Quilts of the Southwest " by J. Michelle Watts. The technique is described in her "Latilla" quilts.
Take a piece of muslin for your backing fabric. Iron it as any fabric after washing and drying to shrink it. Sew the end piece of your strip fabric right side up. Next place the next piece right side down on top of the first piece, lining up the edges. Sew your 1/4 inch (or whatever you want the overlap to be)in place. Flip it over and iron. Add your next piece good side down, sew the 1/4 inch overlap, flip and iron.
I plan on doing this but sewing the strips at an angle. And yes, I am planning on something in the region of 36 or 72 inches.
tim in san jose