What about infrared cookers? They aren't great for cooking dishes that require the boiling of water, which is where microwaves excel, but they do cook things like meat quite fast. Commercially available infrared cookers are rather bulky, but you could easily remove the light and use some kind of light, flexible container to cook inside. I'm guessing the power consumption would be minimal compared to a microwave, so you could get away with a much smaller battery.