Cue Remy working from home, cue me calling every vet in a five-mile radius (there are a surprising number of vets in a five-mile radius of our apartment). Most were either closed or booked solid. We finally found one in the Strip District that takes walk-ins. So at around 11:00, after we bundled ourselves up, we bundled Rochester up in a towel and granted his very dearest wish.
He got to go downstairs, outside, into the backseat of my car. Remy sat there and held him while I drove. He was trembly, but didn't cry or void himself the way he normally does when confronted with an automobile trip. At the vet's office, he sat calmly in our laps even as all manner of large dog moved through the waiting room.
He was well behaved during his check-up, too. The vet was impressed by his size, as most people are (15 1/4 lbs, fills up our laundry basket when he lies in it). Fortunately, the vet didn't find any obstructions or any overt problems. He gave us antibiotics and special food, and we'll need to go back in two weeks if things don't improve. Hopefully, though, Rochester will be fine.
On the car ride home, Rochester was even more docile, and was dutifully rewarded with catnip upon our return. I don't think he meowed even once the whole time. It gives me hope that, if/whenever we do spawn, we will be able to teach our sprogling to be well behaved in public. Sadly, Sephie now smells Vet and Other Strange Things on Rochester, and is being all hissy/growly when he tries to cuddle with her. Hopefully, she'll get over it soon.