I have perfected the dual layer design. Here is the result:
Front (ground layer):
Back (Mirrored):
The power supply is supposed to connect through a barrel jack identical to the one on the Arduino (this should be soldered onto the LED cube driver board's front). The MOSI, SCK, SS and GND of the Arduino are supposed to be connected via standard pins (breakable pins soldered onto the front of the circuit, either male or female). The anode planes and cathode columns are supposed to be connected to the board via standard pins (male/female pin headers soldered onto the front of the board).
If any of you guys want to try producing a real board from the design, I'm happy to send you the Sprint Layout file or some exported results (PDF, Gerber file, drill data, isolation milling, PCB outline milling, etc.). Please keep in mind that this has never been tested (except virtually inside Sprint Layout), so there's a chance that it has some bugs 