The mystery deepens. We got the rig out of the service shop anticipating jumping the starter board to get to our next stop in Bend, OR. The coach started right up and never even hinted of shutting down the entire trip. I have no idea what changed. The rig was stored overnight inside (the problem has seemed to manifest in the morning when its cooler and humidity level are higher) and the shop removed, examined and re-installed the board. Should we have problems on the next leg, I've got the jumper and will have a replacement relay available.
FYI, I would avoid Gordon Truck Service in Olympia, WA. They claimed that they spend 10 hours on their diagnoses and never even sent an estimate for the repair. While I think their diagnoses may have been accurate, I don't believe that they spent anywhere near that amount of time on it.