Anyways, we went back to the post office the next day to check the unit out indepth, and learned a lot about how it was built, and why things were where they were.
It turns out that those York units have these sensors on each compressor called "motor protectors". These motor protectors monitor the temperature of the compressors. When a compressor reaches a certain high temperature, the motor protector sends a signal to a relay, which in turn deactivates the 24 volts running to the contactor, in effect killing the power to that particular compressor for 30 minutes, which is long enough for the temperature to drop. The other compressor is able to run this whole time supplying refrigerant to the indoor unit as usual.
It took 5 billable hours to figure all this out! These motor protectors are great, but they pretty much keep a compressor from burning up because they will never let it get to a temperature that WILL burn it up. It can't burn the circuit out and open it up, so it just lets the compressor run for a shorter and shorter period of time until it just runs long enough to heat up (maybe two minutes) and the sensors kill it. It won't blow up, and it will be forever until it actually opens up the circuit.
So, we figured all this out, and learned that the unit hadn't been cleaned in sometime, and that the ductwork had been pinched almost in half so some other crazy HVAC contractor could install an in-duct furnace that was too small for the necessary airflow.
I'll keep going tomorrow about this.