switched power was showing .03 V.

This sounds like the root of the problem to me. Switched power should not show any voltage at all, positive or negative.

The only way I can envision the player waking up from full-power-off mode in the car is if it's somehow getting voltage on the switched ignition wire.

Are you absolutely certain that the wiring is correct? I've heard that recent VWs and Audis can have some pretty goofy wiring connectors, and also I've heard that they changed the pinouts recently. You sure you didn't wire it with an aftermarket harness plug that expected a different set of pinouts, perhaps for a different year of Audi?

For instance, is it possible that you've wired the switched power wire to something that isn't really switched power?