You are really the only person who can asnwer "what is plausible" because you have the gear lever. My concern is that there is a lot of play or bounce in a gear lever mechanism.
I don't think there is any substitute for experiment.
I have never used hall-effect sensors and I have no idea what their range of activation is.
The mini-joystick is an interesting idea - or just a pair of potentiometers with a suitable linkage. They have the advantage that you could allow for a fair amount of slop so that no possible movement of the gear stick would move the pots to the end of their travel. All that would be needed is for them to give distinctly different readings at different positions.
...R