I know my 2200 works with my 2019 air-conditioner without any modifications, my understanding is that for the 2000 to work you need to install a soft start on the the air-conditioner.
My Honda 2000 runs the unmodified air conditioner on my 2015 Escape 19. Of course, it will run only the air conditioner so other uses such as battery charging must be turned off.
Our WEN 2000i with bonding plug runs AC on our 2015 19 with no issues. However, Jon’s tip about switching the fridge to propane only before running the trailer on the generator we can second. Generator really messed up our fridge for about a week when it was left on auto when using the generator.