Sounds like you've pretty much answered your own question.
Now, look at the technical illustrations in the service manual to see just where all those little motors are.
Disconnect one at a time, until you figure out which one is the culprit.
Replace that one yourself...two screws, an electrical connector, and some fiddling, on your back with a drop light or flashlight.
This area of service manual: http://iihs.net/fsm/?dir=336&viewfil...oor%20Door.pdf
Note: You must look in service manual on different pages to show various mode door actuators.
I believe there are four:
Temp Blend Door
Air Inlet Door