Thank you for the suggestions, I think I got it.
I bought some extender cards off of Ebay then used them to get access to the 150 Watt power transistors on the motherboard. I have this nifty transistor checker from P!ke in the UK, and I found a faulty A62Q3 Darlington transistor that regulates the +20V supply. This supplies a reference voltage to the +12, -5, and +5 volt supplies in a foldback current limiting architecture (at least I think).
I replaced A62Q3 and tested. At first it shut down after 15 minutes. Bummer. Then I ran it again a few more times and at last check it was running for a total of six hours.
So I am far from an HP 8340 expert, but a few extender cards, a multimeter, a transistor checker, and a tenacious can-do attitude sometimes gets the job done!
Thank you again, let me know if your 8340 has problems, I can give you suggestions.
Kenn