Ok, here's my latest update.
Backstory:
My 7000 Marquis (gas) has been shutting down randomly WITHOUT generating any error code. As documented in my posts above, the unit would shut down abruptly as though someone had pressed the stop button. The reported error code was always an old code from a previous abnormal shutdown (i.e. low oil, fuel delivery).
Discovery since last post:
I removed the control module to inspect it carefully. The open side is filled with a clear epoxy/silicone material designed to encapsulate the circuit board and keep it dry. There were several pronounced cracks in this silicone in the corners. The cracks were deep enough to reach the PCB - and in one corner, the board and silicone were rusty colored (picture attached).
Actions:
Figuring moisture ingress was the likely cause of the intermittent shutdowns, I carefully and methodically stripped the silicone off of the board using a small flat-headed screwdriver. The glue came up surprisingly easily. I was unable to remove the PCB from the housing since the glue between the board and the housing was inaccessible. I then put the the module in my toaster oven at 175 deg F (no, I'm not kidding). I let it bake for an hour. As soon as it came out, I filled it with clear GE silicone II caulk from Home Depot for about $6 (picture attached). I let it sit overnight. The following morning, I reinstalled the control module in the genny, and let her run.
Results:
It's now been running for most of the morning without a single shutdown. While this doesn't mean anything (the random shutdowns sometimes went many hours between events), I'll let it run all day (and into the night if need be) to confirm that the shut downs are eliminated. I will post back my results once the testing is completed.
Given that my situation seems unique (shutdown without error code), I don't know how much my troubleshooting will help anyone. However, at a minimum, if you've performed all the possible diagnostics and are left with replacing the ECU, before you do, inspect the sealant carefully. Unless something is toasted on the board, you might just be able to revive it.
I figured I need a new board anyway - so I'm not going to break it more than it's already broken. Besides, I can learn more tricks this way