Thanks again to everyone offering suggestions for fixing my Apple III's
power supply.
I opted to do a wholesale replacement of the electrolytics in the power
supply, since I was likely going to be removing all of them to test them
anyway and there's only a handful to take care of. $9 worth of parts
later, the issue seems to be resolved -- the system powers up and runs
diagnostics. (Though it keeps cycling, so I don't know yet if that's
another problem or normal behavior :)).
The only thing I have noticed is that there's a very noticeable "hiss"
noise coming from the power supply -- not sure where, exactly. Any
ideas if this is normal? At the moment I have only the motherboard &
256k RAM expansion running (no keyboard or floppy drive.)
Thanks again!
Josh