What would it take for me to build something similar to the mockup below?
Well, not much, really, the biggest problem is making it look nice, if you can handle that, then the electronics and the firmware ought to be relatively easy to handle.
I'd use a small 8bit AVR with a bunch of analog inputs, like an ATmega168, but that's pretty arbitrary and based on what I have in my parts drawer.
You could use one of the new AVRs with built in USB, but as MIDI is so low bandwidth, you should be able to get away with using V-USB.
This project looks like a good place to start research: http://cryptomys.de/horo/V-USB-MIDI/index.html
I have my DIY controller running into Max into an app that generates 8 MIDI CC values and sends them out. I already try it and work perfectly.