The four soldered-up button pads, with the button-press-related wires hooked into the vias:
I need to add inter-pad connections like this so that all the boards can be 'reached' by the arduino:
I'm not sure how to arrange that, mechanically, at the moment. Can anyone see how unsped has done it in this photo? I can't quite make out how he's attaching two cables to single vias along the outside edges of the boards.
EDIT: Unsped explains that, for the edge vias which needed more than one wire attached to them, he first soldered male header pins in place, then soldered the necessary wires to those pins. Finally he covered the pins and the joints with liquid plumbers tape to prevent short-circuits. He adds that if he were to do the project again he wouldn't use header pins, but instead solder one wire pushed through the hole, and then solder the second one onto the pad created by soldering the first.