Normally I would rather put up with the heat than listen to the generator noise. You are looking at especially noisy generators.
You might want to consider linking together two very quiet and light 49 pound Honda "2000" generators, rated at only 1,600 watts, they will produce 2,000 watts for 30 minutes, and a pair of them can be connected together for a 4,000 watt limit, and will start a 16 amp air conditioner.
I was reading about one camper, and they bought a 3000 watt Honda from a local dealer, tried it with their rooftop A/C, and found it starts it. However did not restart it (with a need for more energy on a hot day) when it was hot out, so took back the A/C and returned it to the dealer, picking up a pair of Honda 2000 and a kit to link them together.
You might want to check prices and noise levels at this site.
Mayberrys.com Fred.