I like your experiment. It's very interesting.

My water heating theories:
-the base should be as wide as the flame (efficient conduction).
--Flame lapping up the sides is wasted heat.
--Flame that doesn't reach the sides leaves water that isn't coming in contact with any heat (except through lateral convection).

-taller should be better for retaining heat. That is, the heat is applied to the bottom and must pass through the water before leaving out the top (vertical convection). Thus heat stays in water longer. This is consistent with my first theory.

-thus the flame should be matched to the pot

-finally, a windscreen helps ensure that the heat is focused on the pot, and helps reflect some heat in also. Care must be taken not to suffocate the flame.

I also suspect, and you confirmed, that in the real world the differences are negligible.