Our 17-plus year-old beagle didn't think it was time to check out after all. Though all the symptoms we saw yesterday left us concerned she had possibly suffered a debilitating, possibly terminal, stroke, seizure or cranial bleed, a visit to the vet determined she has an inner ear problem that, with medication, can be solved in a week or so.
Neurological tests showed that Molly has "Canine idiopathic vestibular disease", often known as "old dog vestibular disease", for obvious reasons, though she might get ticked if she found out you thought she was in her declining years. Our veterinarian kept Molly on site through the day, reporting she was "doing very well", was cooperative and quiet, arguably the best patient they had.
Quick Googling on Canine idiopathic vestibular disease turned up some promising data, which says we can expect improvement in 72 hours, and full normalcy within 7-14 days.
I picked Molly up around 5:30, paid the bill, in the $200+ range, and took her home in time for her to get dinner, and a new treat, Benadryl, which has already got her extremely relaxed, catching a nap on our loveseat, covered in an Oakland A's blanket. Kristine and I will also team up to administer ear medicine for the next two weeks to help nurse Molly back to health.
After yesterday's scare, we know this dog isn't going to be around forever, but she looks like she'll stick this out and wait until the next crisis.