Agree with taking this thread to Tech Issues. Also, check smokstak.com, which has space dedicated to Generac gensets.
I can add that our ONAN 4KW unit seems to run fine, but it will not carry as much load as shore tie to a proper 30A campground pedestal. 4KW works out to about 33Amps, so the genset "Should" match a 30A campground pedestal.
The generator won't usually carry both the 15K A/C and the Microwave and campground pedestal usually will. If I had to guess why, I'd venture that the genset has monitoring built into its logic board and that monitoring is very conservative so it cuts off at first sign of voltage or frequency drop. I don't have any kind of energy management system, so campground voltage can sag if it wants to and won't be automatically cut off.