Correct about Rheem – at least, that’s the impression I got.
To reset the White Rogers controller (which White Rogers couldn’t help me with…):
After the unit has been off for at least a minute, plug it in, turn on the switch; within a few seconds, depress both arrow buttons on the controller, and hold them until the left light begins to blink. Release them, and within a few seconds, push those arrow buttons in the following sequence: L/R/L/L/R/L/R/R. This should reset the controller.
It took a while to track this information down, but hopefully it will save someone else from the need to purchase a new water heater.