These are finally mine!!!!! Full story and more glorified pictures here.
pyrexlove, the oldest sets from the 1940s were not numbered, with only ‘T.M. REG.’ in an arch above ‘PYREX’ horizontally in the middle, and ‘U.S. PAT. OFF’ below in an up-facing arch.
Here's a picture of the bottom of one of my bowls (I didn't clean it yet so you could read it). Could this be an older set??