You may have two problems. The ECO should shut the water heater down at about 180F. Apparently yours isn't doing this. I would first look to make sure both the thermostat and ECO are in good contact with the tank. Make sure the springs are in place to help force the sensors against the tank. Normally, the thermostat will fail to open the circuit and then the ECO will shut the system down. If the ECO shuts it down, the WH won't relight until you cycle the switch.
I don't know if a bad control board could cause this problem, but you could light the water heater and then pull one of the thermostat wires, the WH should shut down. If it doesn't then your problem lies elsewhere and I would suspect the control board.
You can test the sensors by placing them in hot water and using an ohm meter check to see what temperature the contacts open but given the work involved I would just replace them. You have to take them out to test them and the cost for new sensors isn't that high.