How do I remove this shower stem valve?
The plumber came out today and showed me how to remove it. The Evil Greebo was right, the stem itself unscrewed. The plumber took off the handle and escutcheon, then put the handle knob back on to further unscrew the stem. He did this very slowly and used a lot of force. He had a lot of difficulty with the cold, and that is the one I had started with, so it is not surprising I was doubtful of this being the way it was supposed to work.

The plumber thinks it is Sterling, because those were popular around here years ago and they were low cost, the type that someone would put in the downstairs shower.