make sure you have the refrigerator running on propane, make sure the hot water heater is running on propane, not electric and as a last ditch effort you can throw the breaker for the battery charger. I would expect that gen to run the AC. I have a different 2K generator and never had a problem, but all my camping is at Sea Level at the beach :)
EDIT: after reading more posts, I feel I do need to point out that my red 2000 runs my 8800 btu AC on my arctic Fox great, even on eco mode. and I have mine wired so thermostat turns on both AC AND fan the same time.
I can also leave the battery charger running at the same time but by the time of day I would be running my AC I have already gone through a full solar day of charging batteries so not much load on charger.