No cartwheels just yet, but it appears that the control board may be okay. I had tried cleaning and re-crimping all external connections to the board, but some thing unusual happen the some weeks back. The generator was running while I was puttering in my shop. I went into the basement, where I'd also been working and when I came out the unit had shut down, on its own. I don't know that I'd ever seen this before, unless we were out of fuel or something along those lines.
I immediately had some suspicions. When I attempted to restart, it fired up normally, but stopped as soon as I released the starter switch. I'd recalled reading about this during prior trouble-shooting efforts. The unit has a low pressure oil switch.
So, there are/were a number of possibilities: 1) bad connection (the switch is right above the oil filter), 2) low oil pressure, 3) bad/stuck switch module, 4) problem with oil bi-pass valve. Anyhow, when I grounded the switch, the generator started normally and stayed running. I drained and replaced the oil (it was not low), cleaned the spade terminal at the switch and fired things back up. It has run normally since, and so I tried swapping the original control board back in place and similarly it appears to working as intended.
I'm going to keep an eye on it, because with nearly 10,000 hours on the engine I suppose low oil (due to wear) is a real possibility. I've had it running several days, all day; I'm cautiously optimistic.