I've had success cleaning the carb on an older Onan BGE, by only dropping the bowl.
For a BGE:
- remove the bowl (screw at bottom you mentioned)
- Float and bottom of jets are exposed.
- Remove screw that holds float hinge pin, remove float and float valve. Inspect float valve for any indentation, clean with spray cleaner.
- Spray carb cleaner up float seat, pilot jet (this is your problem based on what you described), main jet.
- Blow out with compressed air, maybe repeat the above.
- Remove the fuel line at the carb, and spray in there also.
Reassemble and see if that resolves the issue.
Other things I've tried with success:
1- Drain the bowl and re-assemble, remove the fuel line and fill the bowl with spray carb cleaner and let it soak.
2. Fill an outboard fuel tank with 1 gallon of fresh gas, add full bottle of Seafoam. Rig the fuel tank to the generator, start the genny and run the gas/seafoam mixture through the carb until it runs smooth.
I never tried removing the pilot jet. If it's got a flathead fitting, remove that and clean in "real" carb cleaner from a can, and then clean with compressed air.
Trying the above was worth the risk for me, worse case I would have had to buy a new carb which I would of needed to do anyways.
Good luck.
