I glued in the analog sticks and soldered the corresponding wires to them. I then wrote a program to turn the leonardo into a USB joystick with 14 buttons and two analog inputs and fiddled around a little to get my code working with those analog sticks.

Also, to connect the pi to the leonardo later on, I took an cheap, broken µUSB cable, and got the µUSB part of it and soldered the wires coming from the pi to for easy plugging in: