If you are using the pot (sensor) from the pedals and hooking it up to the control chip of the joystick, I know whats wrong.
The Pot is a variable resistor, most of the ones used in pedal sets are either 20k 50k or 100k ohms. this means that over the entire rotation of the pot, the resistance changes between 0 and what ever the pot is rated at.
If the joystick pots are rated at 20k and the pedal set pots are rated at 100k you will only get about 1/5th of the actual travel. This is because the joystick is looking for 20k at max resistance, which the pedal pot is going to provide at only 1/5th a revolution. That is of course if the controler is using simple resistance metering/voltage based. In which case the pots will only have two (2) wires going to them.
If the pot has three (3) wires then the controler is using the pot as a voltage divider, in which case you could use any pot since the controler is looking at the in and out voltage, and then using the inbetween from the variable resistor to find out where along the axis the pedals/joystick handel is.
Since you are getting only a quarter of the distance, your using a joystick that uses the first method, and all I can suggest is that you find out what resistance pot the joystick uses, and then get one of the same resistance and put it into the pedals.
Edit: Ignore all of the above unless you want to know a little more about how this stuff works.
now that you posted a little more info, you need to use a pot with a larger turn radius. find one with the same resistance and has 300 degrees of rotation.