Thank you for your reply. I am amazed at some of the things people on this site know about. The original handle was Only about 300 mm and the current one is 800 mm, so changing the handle still would have been worth it by your measurements of what is ideal. I don't doubt that cutting down a tree with it will be a painful experience, so I hope that any one that I have to cut down is small. Also, at 193 cm, I'm pretty tall. Occasionally, I have chopped down trees right at the base, and having the full handle length available to me was handy so I did not have to bend down too much. (My understanding is that all adults have their hands about the same distance from the ground, FWIW.)
Given that E= mV^2, (energy = mass times the square of the velocity), I would have thought that a longer handle would have made the axe head faster and therefore have more kinetic energy to be converted into cutting the wood. But, it is an empirical question, so maybe I will find that the handle is too long.
Another option is those chainsaw-chain-like survival things that people can use to chop down trees.