does the 6" pinwheel mean with or without seam allowance?
Your 6-1/2" squares came out 7-5/8", so 1-1/8" larger than it started. Try cutting your squares 1-1/8" smaller than the size you want it. You can do it with paper and sew it so you don't waste fabric trying it out. If it is only a little big, I'd make them bigger and square the blocks down to the size you want. Be sure to starch your fabric before you cut - you'll have a lot of bias edges.