While bad capacitors usually perform better as they warm up, it's still entirely possible that they're just too far gone. Even if they are not the problem currently, it's a good idea to replace them unless you have an ESR meter and can verify they are in good health.

The fact that the adjustment makes no difference does suggest something else is up though. Check closely for cracked solder joints at the pot or nearby components. Sometimes these can be hairline fractures between the pin and the solder that are *really* hard to see. Try poking and prodding with an *insulated* stick while monitoring the voltage and look for spikes. Also check the pot itself, it's possible to have a cracked track or broken wiper.

Has anyone ever found or created a schematic for these power supplies? That would help with suggestions. I do need to re-cap mine at some point at which time I can poke around for likely culprits. Normally one of the outputs will be fed back through a voltage divider and compared with a reference. One output is regulated directly and the others follow by being wound on the same transformer.