I believe code 37 is wrong frequency/engine RPM. When my Onan 7000 had this problem, it turned out it was running on only one of the 2 cylinders, the rocker arm was bent (cracked) and so not opening the intake valve at all of one cylinder, that cylinder was cold, the other hot, when running. It was difficult to start with this problem, I had to push the auto choke open it get it started, but it would run and generate power till the load was too high to run at the correct RPM and it would stop with code 37 showing. This occurred with 675 hours on the generator. Replacing the bad rocker and re-aligning the others solved my starting and running problems. I repaired myself and was at most a 2 hour repair as both rocker covers are easy to get at. The replacement rocker and 2 rocker cover gaskets where about $25 from Onan. It appeared the rocker broke because the rocker stud became loose on the cylinder head and rotated out several turns.
Ours is a National Dolphin with basement AC. All gas National RV's with basement AC/heat pumps came with Onan 7000 generators, it was not an option. The basement AC with both compressors running uses 3000 watts. If the Onan 5500 generator had been used, that would leave 2500 watts for other things. If the electric water heater element and microwave were both running (1500 + 1200 watts) that could blow the generator breaker. You would really need to manage your power use with a 5500 watt generator.
We also have never had a heating generator problem with our previous 05 and current 08 National Dolphins with the Onan 7000 generators. We did once have a problem with the generator stopping in hot weather but it was the generator electric fuel pump stopping (seizing) when hot and was easy to replace.
This is just my opinion, but it sounds like your have taken care of your generator and I would be surprised if it really has the problems listed other than the bad rocker arm. And, by the way, others have had a rocker break as well, and even more have had fuel pumps fail.
