This is not quite what happened.
About 10:00 yesterday, while I was packing up the car, Andres came out to tell me something. "I think Hera's had a stroke," he said. So I went back inside, and yeah, there is one distressed rat with a nasty head tilt and no balance. So she and I went off to the vet's office to wait for the vet to be free between appointments and he called people to let them know what was going on.
There are a few things this could be: a stroke, an inner ear infection, or a pituitary tumor. The otoscope at the vet's isn't small enough to see into rat ears, so there's no real way to tell which it is. If it's a stroke, she'll either get better in a few days or, eventually, figure out how to walk more or less straight with a crooked head. If it's an ear infection, we've got her on antibiotics now and it should clear up within a couple weeks (although inner ear infections can be hard to get at). If it's a pituitary tumor there isn't really anything we can do, but that's less likely than the other two so I'm trying not to think about it.
We also have a recommendation that if she's being distressed by the vertigo we can get some Bonine (same as Dramamine and a bunch of other trade names; didn't do me any good on the cruise, but they give it to rabbits so maybe it'll be helpful) to try and give her some relief, but she doesn't seem to be too upset about it now, so we'll wait and track some of that down if she gets any worse.
We actually got in to see the vet pretty quickly, so Hera and I came home and I gave her her first dose of antibiotics and we went camping anyway. We had less time to hike than planned, so

So it worked out okay, but whew. Big mess of a worrying day there.
[1] My car is the big cargo-hauling vehicle of the bunch. My car is a Corolla.