I just picked up a champion 3400w inverter here for camping. $750Cdn. It started our 15k btu AC while running the battery charger and lights in our trailer. The AC alone is listed as 16 amps continuous and 72 amps inrush current while starting the compressor. It has an eco setting to idle down and can be parallelled with another one as well to provide 50 amps:
https://www.championpowerequipment.com/product/100269-3400-watt-inverter/
the only downside I can tell is a 1.6gallon fuel tank, but there is a dual fuel version as well that can run off a propane tank (of whatever size you want):
https://www.championpowerequipment.com/product/100396-3400-watt-dual-fuel-inverter/
These seem well received with champion having a large enough network of dealers/service.
https://www.championpowerequipment.com/product/100269-3400-watt-inverter/
the only downside I can tell is a 1.6gallon fuel tank, but there is a dual fuel version as well that can run off a propane tank (of whatever size you want):
https://www.championpowerequipment.com/product/100396-3400-watt-dual-fuel-inverter/
These seem well received with champion having a large enough network of dealers/service.