Sensoring gokart pedals?
Why not use a throttle position sensor from a car?

They are robust potentiometers designed for the job, available in a variety of mounting styles. Some operate directly on a spindle, some have an arm or other mechanism that lends itself to using a control cable or linkage.

Many modern cars the accelerator pedal itself is just a potentiometer, you could mount one of them under the pedal.

Edit to add: Air suspension height sensors often work the same way and have handy actuating rods, P38 Range Rover I know specifically are suitable.