The wiring now requires just three data pins instead of the previous 12 data pins, and results in a completely addressable screen:
There are two chips on that board: one controls the rows and one the columns. If I added a third, and a mess of more wires, I could use the full red/green capacity of the LED matrix. Sadly, it's getting tangled. I think if I learned to solder it'd be possible to get all three shift registers squeezed under the matrix for a nice little screen module:
Anyone out there willing to spend an evening showing how to properly connect components to a prototype board? I can't get back to this stuff for a little while anyway, I think I may have fried the controller on the Arduino somehow.