Well swapping in the capacitor does seem to have fixed the second bad 12V PSU, it's piping out 12V happy as can be, even when transmitting.
Also it's not making the buzz noise anymore and the output's cleaner, too. (Went from like close to 100mV AC leakage to a few mV that go to zero once there's an actual load on it.)
Now just to let it run for a while, see if it keeps working.
(This isn't the one that POW!ed on me. This is the one that worked fine for a few weeks then got weird, and I found a large and apparently _very_ important cap that was very much off-spec.)
