Well, what do you know. After about 15 minutes of fruitless attempts, a reset while connected now does work.
I wonder if the battery needed a little recharging, or at least if the device somehow *thought* it did. Because it can't possibly have been empty, I don't think I've ever seen the battery indicator below 90%, and besides I hadn't used it all that much (read one or two books, a couple of hundred pages, nowhere near a 1,000 let alone 7,000).
I'm really starting to pine for the e-readers two generations down from these current models...