Yes, sheets can have a higher thread count. That's why some long armers won't take them as backings. If buying new, look for the lower counts, like 200. Having said that, I've used them to piece and as backings and they worked just fine. I agree with your comment on them not shrinking & running, and they are sooo soft! Just experiment a bit with your needle size for FMQ. Try a sharp needle and try ones that are larger and smaller to see what your machine likes.