Coming back to note that this resolved itself after disconnecting and reconnecting the unit to multiple computers, a few times, and also moving all the levers top to bottom and back a few times (while connected).
The problem followed the unit from computer to computer at first, which made me think that something had gone bad with the hardware after all, but then all of a sudden it went back to working normally (and indicating normally in the control panel and the setup window).
So…in conclusion I have no idea what happened here, and whether I should expect it to recur.
But if you find this thread because it’s happening to you, you aren’t the first.