Finally found the time to complete this repair. The initial gear position and diagrams are attached. The PDF file also gives the part numbers for anyone who needs to buy the new gears. Cost is less than $30 for the plastic parts.
I think I have also discovered what caused this problem. When I pulled out the cabin air filter, a bunch of leaves, small twigs and other debris was clogging the fresh air flap opening, which did not allow the gear and actuator to close it properly. This is probably what caused the actuator to skip gear teeth as the white gear was trying to turn the black gear(see previous posts for photos) but the black gear which controls the flap, had no where to go.