Okay, diabloNL's instructions got me out of the woods, but the loop went on long enough that now my battery is drained.
I think I've decided from this little experiment that the Reader certainly
can drain its battery in less than 3~4 weeks. I was at 2 blocks when it started and an hour of trying to update its firmware (before I knew how to fix it) means that it's flat now. So I guess the silver lining here is that I've demonstrated that there is a fair amount of power management going on in the Reader under normal circumstances.
BTW, I've added diabloNL's unbricking instructions to the Wiki, so they'll be easier to find
next time I want them.