All right, so I think I've isolated that the problem is caused by the combination of the crank taper and the BB axle taper being forged/machined slightly off-kilter. Here's why I think I've isolated that:
I marked the area of the crank spider and chainrings that was closest to the frame in the rotation-wobble.
I removed the crankarms and rotated them 180 degrees on the BB spindle and re-tightened them. Just to check. The wobble was gone.
To make sure that this wasn't simply a function of the crankarm being pressed onto the BB axle at a slightly wrong angle, I re-rotated the crankarms 180 degrees (back to their original position on the BB spindle) and the wobble was back again, same as before. Then I re-rotated them 180 degrees again, and again, the wobble disappeared.
The crank in question here is a used Shimano 600 130mm-bcd double crank, from around 1994, but the tapers appear to be in good shape. The BB was a brand-new Nashbar-brand (made by RPM) square-taper. I'd be very, very surprised if the BB spindle was bent.
I'm going to try and re-mount the crank on a couple of different bottom brackets (Shimano UN-73 113mm and 107mm) and see if there's wobble.
But at this point it appears that there's slight variation in the taper angle with both the crank and the BB spindle, probably as a result of manufacturing.