An electrical engineer friend of mine mentioned a way I could test to see which (if any) of the spare wires to the thermostat go all the way through.

After making sure no current is running through them, short the wires on one end (say, at the furnace). Then, using a multimeter set to short (or continuity) mode, test the wires to see which ones go all the way through.

The other option I’m looking at (and almost appeals to me more, to be honest – for a variety of reasons) is running new wiring for the thermostat and installing it in a different location. I have a location in mind that would have easy access for me without having to run the wiring THROUGH walls, and without it being exposed to people. It would also place the thermostat into the main room of the house and get it out from behind the entertainment center (where the current one is), avoiding the heat buildup from the equipment there (and avoiding having the system start up when it doesn’t need to).