2000 watt peak inverter generators is what I have used for close to 5 years now. I have had the largo big burner (says 8-12 gpm, really max is 8 gpm) for 4 years running off these small generators. Start the inverter up, give it 30s - min of warm up, switch the burner, turn it on eco mode and work for 10 hours on a gallon of gas.
I would recommend 120v over 12v in your situation, also would keep in mind with the bigger burner you can drink diesel quick. Turning the heat up, I can run through a tank in 4-5 hours no problem, keep that in mind if you are using lots of heat, you will need some extra diesel.