How should I hook up my WiFi thermostat given my current wiring situation?
After doing some research and physically tracing the wires, I was able to confirm that the white cable labeled "??" in the diagram was indeed going to the outside compressor unit. Hence it looks like the Blue wire was being used in place of the missing Yellow wire. As a result, my solution is to rewire the Blue to the "C" terminals on both end and then run a yellow 18 gauge wire to where the Blue one used to be connected. That way, the wires are connected as they're colored.

I'm guessing the Y terminal on the furnace is probably to control the fan speed for cooling mode, but since the A/C works now I'll leave it as a separate question.