Check for loose/disintegrated vacuum lines as well. Could be getting a big gulp of unexpected air when its trying to move the blend door.
Very good point about vacuum.
You could confirm if this is it by plugging the vacuum source at the manifold, then run the motor and move the adustment control as before and see if the engine stumbles or not. if the stumble issue resolves, but then reappears once you restore the vacuum, then you will know with great confidence that you got a vacuum issue.
On a side note...
My friend had on old 1956 T Bird back in the day in the 80s, drove to Vegas from west coast in it. That T Bird had a vacuum wiper system, it leaked, engine ran poor when operating the wiper. AND just when you needed the wipers to run fastest, at accelerating, or even cruising at freeway speed, the vacuum is really low in those engine operational regimes , so the wipers slow down, let off the gas and coast, and the wipers speed up as engine vacuum spikes when the throttle is suddenly let up. We had non functional wipers on one road trip do to leaks, raining hard, late night, highway, three of us crammed on the seat. no wiper, but my friend tells me, the driver, that at over 90 mph the wind will sheet the rain off the glass. And sure enough, the windshield did clear up as the needle passed 90.
Crazy how I am still alive no? Oh and the car had a drip from the dash in the rain, dripped directly on the gas pedal foot, no way to avoid it. You drove in the rain, you had a wet right foot! That was some car, collectable nowdays, back then you could still get old beater cars like that cheap. Golly, the 1956 two seater convertible Alfas a friend of mine had in highschool, he bought two of them with money working at a carwash, and a pizza joint, I bet they are high five figure cars now, back then, they were just old cars rather than classics