My power supply is repaired! Thanks to James for reverse-engineering the schematics and Ray for hosting them.
Consulting with a friend, we tested things on the PSU whilst it was powered down and basically ruled out most of the passive parts on the board. All of the diodes appeared to test OK, too (or at least didn't lead us to suspect they were bad). This focused our attention on the various active components that were left over.
I didn't feel confident about troubleshooting a live power supply with my experience and equipment, so, I basically shotgun-replaced all of the comparators, many of the commodity transistors (all of the 2N4404s), the SG3524 switching controller, and the crowbar SCR. Happily, this seems to have worked. I saved everything I replaced, and this afternoon I ran some tests on those parts. Everything that's easy to test appeared to be just fine, which leaves only the SG3524. This is a complicated IC (relatively speaking) and seems like the kind of thing that would take a fair amount of preparation to examine, so for now I think I'll just set it aside. I did hook up Vcc and ground and checked the reference voltage output, which seems fine, and the chip doesn't get suspiciously hot, either. If anyone has any ideas of a test they'd like me to try, I'd give it a shot in my spare time if i have the parts.
I can't say my other tests were comprehensive, but for now I suspect the SG3524. It's nice to have the old PSU back; let's hope no part fails that's harder to replace (the SG3524 is still available for sale).