How can I add a C wire with this unusual installation?
If it really is wired like your diagram, there's nothing wrong with the current wiring.   

To add your C wire, simply connect your extra wire to the C terminal in the furnace.  Depending on where the splice of the blue wires from the outdoor unit and the humidifier is, it might be convenient to splice your new C wire in there. 

Warning: You'll want to make sure the transformer in the furnace can handle the additional load of the thermostat. It's not commonly a problem, but sometimes can be depending on how the humidifier is connected.