So we found out a few things - the +5v trickle is dropping, even with that little diode hack. Adding an external 5v power supply to that pin (via a cannibalized BlackBerry charger) works if the PSU isn't installed in the IIci. As soon as it's installed, the same problem comes back.
It's looking like it might be the voltage regulator, or something else. Rather than try to dismantle the IIci PSU (it's a real beast), we are going to replace it with a very similar PSU pulled from an old HP desktop. The form factor is almost identical, so it should be fairly trivial to install the HP PSU's circuit board inside the steel enclosure of the IIci's failing PSU. We'll see!
It's looking like it might be the voltage regulator, or something else. Rather than try to dismantle the IIci PSU (it's a real beast), we are going to replace it with a very similar PSU pulled from an old HP desktop. The form factor is almost identical, so it should be fairly trivial to install the HP PSU's circuit board inside the steel enclosure of the IIci's failing PSU. We'll see!