OK, Jim, I checked the temperature at the kitchen faucet, which is about 15 feet
from the water heater. The hot water lines from the heater to the kitchen are
insulated. With the water on full hot, the temperature after 60 seconds was
124.5 degrees.

I ran a few gallons to make the heater come on. then I checked again an hour
later when the heater should have been heating things to max. This time the
temperature was 129 degrees........

No WONDER my wife can stand there with her hand in the water and not feel
anything close to scalding.......

OK, so I'm going to conclude that for whatever reason the heater just isn't
doing a very good job of heating - whether it be the control, or heater, or
burner, or thermostat, or whatever... Given that the thing is around 5 years
old, I'm thinking its not worth a whole lot to try to fix controls or whatever.
Especially considering that we've got a history of going through water heaters
at almost exactly 5 year intervals. The plumber that put in the second-to-last
one said that it shortens their life to run them on full hot all the time...

So, I'm figuring it may be worth getting a high recovery unit if its not a whole
lot more than a standard one...