The shower water suddenly gets hotter, suddenly goes from 105 to 111F
I finally figured it out, the problem was different from what I thought. The real problem is that 3 of the 4 RP19804 I tried were defective. You could not adjust the temperature in small increments, any small change caused wild temperature swings. Putting a handle instead of a knobs helped a little, but the real answer was to keep trying valves until I found one that worked.