I got SAM-BA 2.16 installed tonight then erased the firmware and re-flashed the board. That didn't change anything. So, next steps were to unplug everything from the board and see if thermistors would work by themselves. This revealed something interesting. If only one of the thermistors (hotend & bed) is connected then the Duet doesn't report any reading at all for either thermistors. However, when I connect the second thermistor then I start getting the erratic values for both thermistors. I've tested both thermistors with a meter and tried connecting new thermistors and the behavior is the same. I now think there's something wrong with this board.
You can see my tests in this video.
Any ideas? Next, I'm going to start ripping my other Duet WiFi board out of my other printer (that's not working because of other issues….) and swap it out. I'm really hesitant to do this w/o knowing why this board is not working, though. I've examined all the obvious locations where there could be wiring problems and so far have found nothing that looks like a problem. The only thing that happened between working & not working was a config change & restart. I'm puzzled...