Your problem is the type of thing I enjoy solving for myself. I made a quilt, one of my first, called confusion. I had seen it on Alex Anderson's program. You sewed patchwork pieces to the sides of the small center and then trimmed them off on an angle by laying your 12 1/2 inch ruler on it. So each square was not straight on when you lined them up, but not exactly on point either. Also if you go to quilterscache.com there are many quilt blocks there and you could use one that had a square center. Two I liked for your purpose were (Page 15) London Roads and Page 11 (sq dance. You can search them by page or by name. i will try a search for the confusion quilt or see if I can find my picture of mine. and will then post it.