I have a 270bh with the same air conditioning unit. I bought an Echo Bearcat 3,500 watt inverter and it runs everything fine. Starts first time every time and very quiet. Half the cost of a Honda. It’s 3 years old now and runs perfect. I also have a 100 watt solar panel which keeps the deep cycle battery fully charged on sunny days.
2017 Sunset Trails 270bh
2016 F150 3.5 EcoBoost Platinum Crew 4x4
3,500w Echo Bearcat inverter generator
100w solar panel
Traded a Jayco X17Z hybrid bought new in 2013.