I was able to nab a remote-canister stove (Fire-Maple Blade 2) and try out the bottle on top of it. While the stove itself is very stable, the bottle stability still isn't great. For this particular combo, the arms have to be folded in and the indented area on the bottom of the bottle centers the bottle, but it's still tenuous.

I don't have an old windscreen to wrap around, and I've found that aluminum cans melt too easily, so I'll have to dig out some flashing or other durable metal to concentrate the heat into a smaller area.

I think this is one of those, 'Don't try this at camp, kids!' kind of situations. Still fun, though.