Quite often a "short to plus" actually means "open circuit" as the diagnostic circuit is pulling the wire to (+) to see if it rises when it shouldn't.
These cars are 12 years old now and the doors have been opened and closed many times. One thing to check would be the wires in the boot between the door and the frame, usually they break near where they enter the door. Haven't seen this on any C7's yet but who knows.
Since all of your codes are for the Driver's door, I would first be determining what ground the driver's door module uses. It is probably near the drivers door pillar. If the ground for the door was definitely good, and the wires in the boot looked good, I'd be pulling the door panel to look at the door module... Maybe it has gotten wet and is corroded? If this is the case it should be obvious.
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