sedstar: first I will say again that throw (defined as the luminous intensity of the beam, measured in candela) and light collection efficiency are two different things. I think you are are focusing on optimizing the light collection efficiency, which, while important, is not the same thing as throw. A light can have a lot of throw but have poor efficiency. For example a light with a large diameter lens and low NA.
Now, regarding whether the throw is proportional to the lens area. I will admit I can’t find any paper describing how to predict the throw of a flashlight. So I can only, again, refer to this thread. That Edmunds optics document seems to focus on light collection efficiency and does not talk about throw. But, again, throw and efficiency are different things.