I just called GoDaddy, my domain registrar, to find out what was up with my domains.
Mark, the Helpful Support Representative (and he actually was helpful), informed me there was already an escalated support case and the NOC minions were working on it. It was marked for resolution "within 72 hours," but, he hastened to inform me, they did not expect it to take anywhere nearly that long—in fact, my domains started functioning again while I was on the line.
But then Mark wondered, in this off-hand manner, why wasn't I hosting my site(s) at GoDaddy? Because right now, today only, and only for call-in customers, GoDaddy is offering a hosting special for just $some-amount-I-didn't-catch per year for sites up to 150 megabytes! And by the way, would I like traffic tools and email accounts while I'm at it?