The new and improved water heater technician came this morning from a different company to look at our water heater. He then spent some time suggesting to Whirlpool that it would be wise to replace the unit, but they (Whirlpool) decided to send another set of replacement sensors instead.
The tech couldn't manage to relight the unit, but I managed to.
However, it was flashing six again this evening and when I went to relight it for hot water in the morning, I couldn't. It does nothing. No flashes, nothing.
I think tomorrow someone is going to get me a replacement hot water heater.
(The new tech, by the way, is quite good, as opposed to the doofus from another company who didn't much care what the flashing lights meant. This is progress.)