Just stumbled upon this very interesting sounding induction stovetop that I imagine would work very nicely in a mobile setup:
Our First Step Towards the Home of the Future - Impulse Blog
It's got a 3 kWh LFP battery pack integrated into the stovetop that can charge over a normal 120v outlet. So it can output higher BTUs than gas without requiring high-voltage wiring.
My only concern would be what happens if you want to cook something over an extended period (e.g. simmering a chicken stock for 6 hours). They say it can last "3 meals" with the power out, but don't say how long they consider a "meal" to be.