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Yeah batteries would probably work. A large battery bank can have 1kwh of capacity, and induction stoves are about 1.5kw. Which means you could run a stove for about 40min. You could bring more for longer. I’m sure by the time you can’t get propane, batteries will have gotten much better too.
That depends on a lot more factors for how dilute it gets. I didn’t know how likely it is for the air currents to dilute the aluminum exhaust over a large enough area before it rains. Maybe someone could do some analysis, but I don’t know how.