OK, so I spoke too soon earlier. About 20 minutes after that, the Westell DSL bridge stopped responding again. I stuck it int he freezer for 15 minutes, noticing it was rather warm; no joy. It's been sitting on the table disconnected for most of the day; I just tried it again, and it's now working again. It's anyone's guess how long that condition will continue.
I guess I'll be swapping in the replacement that Verizon is overnighting us after all.