You can edit input.map & gamekey.map to switch-up various key functions (they're simple text files). Might take a little searching but if you google something like "battlezone input.map" you'll probably find old, or, old, old threads discussing how to do it. Not sure about inverted joystick, try the inverted mouse option, tho I'm guessing that wouldn't make a difference.

Thank you. I will try searching those.