I will need to think about that a while: Alcohol stoves not as efficient at altitude. it seems to me the vapor pressure of the alcohol would higher and that might make it burn fuel faster, but shouldn't reduce the boiling time. If anything reduce the time it takes. The air is thinner, but how much that affects a stove with plenty of openings for make up air...I just don't know. And wouldn't that be the case for any stove? Thin air would reduce the efficinecy of a gasoline or kerosene stove just as much wouldn't it? And I know from experience at least at 10,ooo feet those types work fine.
Maybe someone who knows more about Chemistry can answer the question why your alcohol stoves did not performe as well at altitude.