There is no specific law to which I refer. It may be rooted in Common Law, but there is no case law that says the police can only defend themselves with guns. As for executions, yes that has been ruled on numerous times by the supreme court, but it’s also a completely different scenario. Self defense versus a contemplated execution by the State, in which the duty of the State is to not inflict unnecessary suffering. That logic has never applied to any self defense scenario.
Self-defense? Dinno. One guy in a cabin surrounded by armed poice? I see no legal or other justification for intentionally burning someone alive. there are more humane ways of wasting an SOB than by burning them alive.