One electromechanical way to achieve this is to add a double pot (i.e. two pots sharing the same shaft) in series with the joystick.
If you can make the pot move according to speed, then one of the double pot would go from the joystick to 5V, the other from the joystick to ground.
+5V----Speed Pot
Joystick
Speed Pot
Ground
At slow speed, the Speed Pot would read 0K. At higher speed the value, the speed pot would read 5K or so (the higher the value, the less left/right control).