How about doing the 31 X 62 with 25 pieces just as you suggest, and then sew the remaining pieces together and add them to the quilt top down one side of the length? I am not a math whiz either, but estimating 15 more strips sewn together @ around 41" + 21" by 2"(when sewn), should add about 14" of width. 45" x 62" is a nice size quilt.