I replaced the top and bottom thermostats on my water heater last weekend. I tested the old thermostats once I got them out but they were reading normal.
I think it was an intermittent failure where the thermostat was sticking and it started "trying to boil" the water in the tank.
Everything seems to be working so far and the water is actually hotter even though I am using the same temperature.
Here are all the youtube videos I used for testing and replacing parts.
Make sure to take some pictures before you start so you can reconnect it properly. Here are the ones I took:
Update: The problem persists despite changing the parts. The problem was not in the house but at the water meter. The pressure regulator was set fully open. After adjusting the pressure regulator down about 50% the water heater problems have ceased. I am hopeful that this helps someone else.