Obviously the key is finding out why the unit is shutting down. I would invest time watching the meter on each sensor until the unit shuts down. If none of the sensors are tripping then you can move deeper into the control systems. If you find that a sensor is shutting the thing down you can go deeper into the engine. If you are patient and methodical you will find the nasty gremlin that has been laughing at you. Good luck
It sure sounds like a control issue but if you verified all the sensors (high engine temp, low coolant level,etc) and replaced control board and fuel pump it sounds like you have covered the usual suspects. This is gas powered correct? If so possible engine ignition issue or connector issue in the engine harness. May be worth it to check/clean all the connectors (following usual safety procedures).
Otherwise try reaching out to flightsystems Inc ( ). They provide/manufacture a lot of replacement parts for generators (electrical and control side) and are super helpful in troubleshooting. They have a lot of experience and may be able to give you some answers.
Sorry hope you get it worked out.
How about the oil level sensor? Is it using or burning a little oil? Maybe try running oil level on the high side.
Here is a link to the service manual and troubleshooting guide. FWIW I've know others to disconnect one sensor at a time to narrow down or eliminate a flaky sensor from the list of possibilities. Need to be confident there isn't an underlying mechanical issue however.
According to the manual the low oil pressure, high coolant temp and low coolant level sensors are all normally open. In which case disconnecting and isolating one of the two wires will prevent the sensor from shutting down the engine.
Manual doesn't specify the high exhaust temperature switch but I suspect it also is NO. If you want to be sure take one wire off and check both terminals with ohm meter. Or just disconnect one wire and see if it starts and runs. If engine stops right away the sensor is likely normally closed in which case the two wires need to be tied together to bypass switch.
Have you noticed which LEDs are lit when the unit shuts down? They apparently cooresond to relays being energized. From what I can tell if LED 4 lights up, that means the control mechanism is purposely shutting down the generator indicating a sensor fault or a faulty start/stop switch, etc. otherwise it could be something outside of the control system such as fuel delivery, ignition problems, anti diesel solenoid, etc. A lot to throw at you but this may give you another clue.
I believe generators were put on this earth to destroy the will of good men who love the sea.