Just my two cents. If you were modifying a more traditional stove, especially if you were changing the width of the base, but even to a lesser degree the height, then I would expect potential efficiency changes because of the way the heated air flows past the pot bottom and sides for a given stove. A good example of this is how different a cat stove will work depending on the ratio of the cat stove and pot diameters.
In the JetBoil I suppose there might be some issue w/respect to that, but in this case the heat exchanger is a constant, and we might assume to lowest order that the rate of heat *flow* into the pot would be more or less unchanged - basically less susceptible to pot shape. I don't find a lot of heated air outside my Sol Ti, so that is a good thing. It means most of the heat is efficiently transferred to the water through the heat exchanger, so for that stove expect the shape to be less of a concern.
I emphasize flow here because there are two different things which I believe you might be conflating in your blog post - heat flow and temperature. You could have a lot of heat flow into the pot, but if the heat is transferred to the water efficiently the actual temperature may not be that great. In practice the having water in the pot will probably be the main thing that will prevent the temperature of the pot from getting too hot. A good heat conductor such as thin metal of any kind should spread the heat rather quickly through the metal, so it would be reasonable to assume if the pot was filled with water the water would act as a temperature buffer. At first the energy of the heat will go into raising the temperature of the water, and then after the water reaches boiling temperature the energy goes into converting the water into vapor at a constant temperature. So to first approximation I would guess that you are not going to generate a higher temperature in the heat exchanger by cutting down the pot.
Just make sure the pot is full of water at all times when you have the stove turned on. However, as many people have learned the hard way, one of the things that makes such pots efficient (a low heat capacity) is the kind of thing that will rapidly lead to a damaged pot if the water is not there. So the pot will rapidly overheat if you don't have water in it, and a cut down pot will burn more rapidly. But since you should never do this, you should not have this issue.
What may become an issue is if you boil so little water the time to boil may become unmanageably short, and maybe you will waste energy. I think turning down the burner a low as possible, as least a well as you can on a jetboil, would help both issues.
I'm not too clear on what you are trying to gain by cutting down the pot. Is it just weight? Or were you somehow hoping for efficiently. I don;t think the latter will change much in this case. The right way to measure is the amount of gas used to boiled a certain amount of water. Here, if I am reading you correctly, you merely lowered the amount of time and fuel by boiling less water. My guess, but you can check this, is that if you simply put the same amount of water in both pots you would used approximately the same amount of fuel and take the same amount of time, so zero change in efficiency, except if you count the weight savings of the pot itself.
I am also not too clear what exactly you want help with math wise. I guess %90 is stating the issue clearly. I'll give it a go if you can explain. In theory I am way over qualified for the job, but that doesn't guarantee anything. LOL
I'm not sure what you meant by 'distance' in the blog article, but is sounds like you are interested in determining the inverse efficiency, or weight carried per boil (for some standard boil like 2 cups (but you can easily convert this later into weight per oz of water, or whatever units you like, including weight per unit of distance using *your* stats on typical distance traveled per boils), in a way that includes the weight of the canister. Others have done this before, of course, but the weight carried per boil would be
R = Wg + (Wc/n)
where Wg is the weight of gas used to do one "standard" boil, Wc is the canister weight, an n is the number of boil you need before resupply, assuming your canister doesn't run out. If you are a true UL purist you would replace Wc with the combined weight of the canister + stove + pot + other paraphernalia like windscreens ans the like for each system (the weight of the whole stove system, and what you will get when comparing a specific alcohol stove with the jetboil will be R curves as a function of the number of boils that will cross at a certain number of boils, and for more than that number of boils the jetboil will be more efficient (less weight carried on a trip requiring n or more boils).
The crossing point will be at
n = (Ws2- Ws1)/(Wg1 - Wg2)
where Ws1 and Ws2 are the weights of the stoves systems for system 1 and 2, and Wg1 and Wg2 and the weight of the gas used for a boil for the two systems. This assumes Ws2 > Ws1, and Wg1 > Wg2 (as would be the case for an alcohol stove as stove 1, and the jetboil for stove 2).
Since it sounds like you have carefully measured Wg for your stoves, and of course you know the Ws, you can use that formula to tell you at exactly how many boils the heavier more efficiently stove wins out over the lighter less efficient one. So you have everything you need to calculate n for your esbit stove (stove 1) and your jetboil (cut down or otherwise).