How would one go about integrating a custom driver setup like here with WPILIB?
The picture you linked is incredibly old, as it shows the old blue driver station box that (iirc) was last used in 2009. A similar setup can still be achieved simply by using a TI Launchpad MSP430 that was included in the 2015 KoP. If you don’t have this, or have lost it, you can find it on FIRST Choice for 10 credits. You can find out how to set it up and how to use it here.
You can use 2 standard USB joysticks.
For the buttons, something like this, which simulates a standard joystick.
We included a usb hub in our setup, so if we are forced to use the Field’s Driver Station, it will easily plug into that.
A similar setup can still be achieved simply by using a TI Launchpad MSP430 that was included in the 2015 KoP.
This is true. The launchpad is very easy to set up and use and can be easily calibrated through the set up usb joystick tool on every windows computer. Once configured and everything is plugged up it gets referenced in code like a joystick.