Hi,
I find it helps cool air distribution to run the roof air with the fan only. That is an easy load for the inverter. About 60 minutes before I stop, I do start the generator and run the roof air.
If I know I'll have shore power, I have sometimes run the roof air from the inverter.
The biggest problem is after stopping the transmission and engine radiate heat into the cab. If I open the hood that helps to let the heat out.
I'm planning a massive solar upgrade, and if it comes to pass I should be able to run the roof air more or less totally on energy from the sun. It may also keep the RV cooler by shading the roof.