Unfortunately the Wii controller was Bluetooth-only and I couldn't even get it to work with anything other than an actual Wii. Therefore it was time to go for the brute force method of reading the button states with a Teensy (a mini powerful Arduino) which can act as a Joystick HID when connected to the RPI through USB.

Luckily the controller board had pads for all the button signals and here you can see them all wired up (except for the analogue joysticks).