Can you check the fuel PSI, could it be too high? Stock fuel pump in there or not?
Fuel PSI has to be very low for an Onan. Around 5 psi or so. Has nothing to do with the control board. It doesn't control fuel PSI, just alarms and other such stuff as forcing shutdowns because of alarms.
Are you getting
any error codes?
The extra fuel on the plug could be coming in just after the engine dies for another unrelated reason. The control board can shut down the genny for many reasons, and many of them can sound like an engine problem. Such as going off frequency and back within spec and out again. The freq must stay close to 3,600 RPMs or the control board will shut down the engine. But such things will show as an alarm code.
About what year is the genny? Older ones may not have alarm codes.
-Don- Reno, NV