Fixed
The problem was the lower thermostat, that last and cheapest part I replaced.
For the benefit of other DIYers I offer the following:
In a double element heater the lower element is primary; it does the bulk of the heating, and hot water rises to the top and the cold goes to the bottom in a convection cycle. I.e. although the bottom element is primary, the water heats from the top down. The circuitry is such that only 1 element is on at a time; the bottom element heats the water up to the temp its thermostat is set on, then shuts off. If the water temp at the upper thermostat is under its setting the upper will come on until its temp is reached. And so on. If it gets too hot the upper limit switch will trip and power will be shut off until the switch is manually reset.
That is what was happening in my case. Now I know that the tipoff was that after resetting, my tenant would get really hot water then have none the next morning. What was happening was that the lower thermostat never shut the lower element off and the temp would rise until the limit switch tripped sometime during the night. I figured this out when I saw that w/ the lower thermostat set at its lowest temp the water at the upper was so hot that the upper thermostat would not kick in even when set on its highest temp.