A 50-60 amp converter is about all the 2k generators can run, It isn't just the watts, Power factor comes into play - which puts the load on the generator far above the amps X watts.. My TH came with a 100 amp converter, I bought an 80 amp unit to run off the small generator, no love - ended up getting a 55 amp for the 2k generator. The onan 5500 runs all three at the same time.
You may notice the generator will run the converter when the batteries are VERY low, (and output closer to 13 volts), but as the batteries get closer to 70-80% the charge voltage is closer to 14.4 volts, and the actual wattage climbs, this plus efficiency losses plus power factor overload the generators output.