Using an inverter to power the fan and other AC loads will likely work. As pointed out the Generator can handle the run load without problem.
I've used this method at work but had the ability to limit charger current. I do not think it would work with my charger because it draws so much and I cannot easily limit the current.
I would try this and just leave the charger off and run the batteries down, and charge them later, or get a small charger, maybe a 10amp and use that one.
Or just remember to shut off the charger when the AC starts.
Have faith that the oceans are going to rise and flood the world, that plague and pestilence brought on by Climate Change is going to punish us for not believing. Please do as they say it is our only hope. :P