Start using them as "leaders and enders" by sewing the 1/4" seam allowance. Later, press and then join them to make long strips. In a recent quilt magazine, either American Patchwork or McCalls, there was a whole quilt made from 1" finished squares. There was a slightly shirred strip across the quilt which added some interest about every 10-12 rows. I don't think I would go the 1" finished route, however, 2" finished might work for me and make something smaller than a full-sized top. Also, the squares were offset one row to the next which would help w/bulk. In other words, one row would start w/a full square, the second w/half square.
Meanwhile, I find my mags and see which one shows this quilt as I know I have it marked.