There are other methods too, e.g. fire inhibitors (like Halon or whatever is allowed now) or shockwave to disrupt fire boundary. But I doubt they are very practical on a spaceship.
First stage (Super Heavy) is flushing the engine bay with massive ammounts of CO2.
Unless I'm misunderstanding you, it's not the same thing at all: in the case you're talking about you're shielding against nominal heat, which is not the same thing as contingency planning to extinguish a fire that shouldn't be there in the first place.
Not an expert but I'm not too sure about shockwave in a confined space.
How does Halon works?