Thanks, all, for your advice. After moving the needle over more and pressing more carefully, I was able to get a 12.5" width, but then the other side of the square was still 12 3/8" (which had to do with my cutting, I guess). Aargh! It was time for a glass of wine at that point. Lol. But then I came back and read your note Jan, and I decided I'll just square everything up to 12 3/8" and get on with it.
By the way, thanks for the blocking technique, Feline Fanatic. I'm sure that'll come in handy sometime.
I found that very very precise cutting and seaming (to the single thread in the weave) invariably gave me smaller blocks than "advertised." Why? Because sewn fabric is not really flat. You have a third dimension: the height of the seam with its sewn threads. I either cut bigger, seam smaller, or content myself with the slightly off-size finished block. The link Paper Princess provided is a good explanation. I would be a little nervous about blocking stitched, woven cotton. I've blocked knitted and crocheted cotton and wool, but I always thought the flexibility of the stitches played a part in that process. Hmmm.