Troutguy , I too start the AC in fan only mode, but only until I hear the fan is up to speed, then I switch to cool mode. I do run the Honda in the "eco" mode. I'm guessing that my solar keeps the battery charge high enough that I do not have to turn my charger off. Do keep in mind, my A/C is a 2004 9200.
My fridge is always on propane, unless I am on shore power, then I might switch to 120-volts. I agree, you can't run the microwave or a toaster while running the AC with the Honda 2000.
You post you don't run the Honda in "eco" mode. Have you tried to run the "eco" mode? Perhaps after your A/C is up and running on cool, you could switch to "eco" mode?
So okan-star, with your research, I understand the Coleman A/C to run today with the Honda 2000 is the Coleman Mach 1 power saver 48207C966 = 9.3 amps at low 9.5 at high 1260 watts at 120 F. or has that been replaced?