I have learned that the vehicle has the ability to remember the most recent fresh air flap position so it can resume this position on startup. I need to learn more about this possibly being part of the problem. This can be deactivated by reprogramming at the dealer. I've narrowed it down to two possibilities, the heater/ac unit is sending the wrong signal to the fresh air/recirc actuator at startup, or the actuator is bad. I've ordered a new actuator. Won't have time to work on the Z for a week or so, I will post any new developments then. In the meantime, if anyone out there has encountered this problem and has any input, I'm all ears.
In the meantime, I have disconnected the 4 wire connector that leads to the actuator that is causing the flapping noise. I can easily see how this problem can lead to broken/cracked plastic gears and other parts(see post above from Jax543210). Especially in the cold winter months when plastic parts get brittle. As stated earlier, my Z doesn't have the broken gears yet, but it is probably just a matter of time. Once those gears break, the repair becomes an entirely different ballgame in that the dash probably has to be taken apart to remove the a/c housing to install new parts. I'm hoping to avoid that.
Disconnecting the actuator has no adverse side effects, other than I am not able to switch between fresh air and recirculation mode without re-connecting the actuator. No dash lights or codes thrown.