Help with gamepad potentiometers

I've been working on a custom gamepad for some time. Basically just rewiring buttons and getting it into a custom arcade type of thing anyway so i want to also include the two sticks and they each work with a 3 pin potentiometer. The original potentiometer on most controllers is a 10k ohm pretty normal straightforward small plastic varying resistor. Now the problem is that when i rewired that to one of those big metal regular ones it only sensed a little less than 180° of rotation rather than the full 270° ish that the potentiometer allows (which is what i need it to do). Now when i tried the original one it would only sense about 30° of rotation even though when i opened it it had the resistance strip and could turn about 270°. I don't have a multimeter so i can't check the resistance of the original potentiometer but the one that i hooked up to it was 5k and i tested that at the shop it was pretty accurately 5k ohm when fully turned. Now should i get one with less resistance or more?

You need to use the same resistance as the pot in the original.

The pic you posted (left side) uses 10k pots.

I can see two possible solutions to your problem.
1, if you can rotate the pot so it goes from 0° to 180° then you can increase the voltage supplied to the positive of the pot. I.E. if the pot is supplied with 6V so it produces 0 to 6V on the wiper then supplying it with 9V will still give 0 to 6V on the wiper.
2. if rotating the pot isn't possible then an opamp could be used with a gain of 1.5 to increase the 1V to 5V output to 0 to 6V output.

Mike.