Thanks everyone for your suggestions.
Bearing in mind (apologies…) the age of the bearings, it seemed a good idea to replace them, so in went a pair of Polish NSK 6201ZZCM. The 'M' clearance rating is supposedly tighter than the C3 rating commonly available here, and is considered good for motors – quiet-running. Chinese bearings avoided – some must be fine, but which?
Motor reassembled with well-greased seal. Silence – for 30 seconds, then Squeeeek. Not the bearings then… With a hook probe, I was able to flick the seal's spring off whilst the motor was running – silence! The seal is a muck-keeper-outer, not an oil-keeper-inner, so the spring is accessible on the outside. So Mark is right – it was the seal! The removed bearings spin 'nicely', but with less grease drag than one would expect, so it was a good idea to replace them.
Inspection of the seal with a magnifier revealed that there was a matt cylindrical land, about 1.5mm axial length, in place of the expected sharp lip. The shaft was unmarked. This isn't a seal failure due to wearing-out, because of such little running time, but presumably due to the spring pressure over 30 years having caused the rubber to deform. Perhaps also long periods of disuse allowed the seal to adhere to the shaft, so that its surface was torn off at the next start.
I've not come across this before, but perhaps it's a well-known failure mechanism. Anyway, the thread is now here for anyone who searches for a solution to a squeaky motor.