So you see nothing on the front of the heater box under the dash, which is
moving with the control?

Would be vac operated as you say, listewn close for a vacuum leak.  Is your
engine idling high?

So there is some door which isn't opening.  You might read my posting about
my '98 Club Wagon, so see an extreme example of what can happen, although I
seriously doubt that your floor-air door has the actuator that is needed for
a temperature blender door.  Nevertheless, my problem was caused by breakage
of plastic.  For some reason, my blender door didn't want to move, and the
powerful impeller moved anyway; something had to break, and that was the
plastic sheath formed by the molded plastic door itself.
I started out hoping to find a failed vacuum line, but that was not the
case, at all.
Your floor door is probably vacuum-motor actuated.  You can get a vacuum
gun, and attach it to the motor, once you find it.  Then you simulate the
actions of your system, to produce vacuum at the motor (diaphragm).  No
movement indicates failed motor.  Conversely, put vacuum gauge on the
controlling tube, and observe; presence of vacuum at appropriate time
exonerates controlling mechanism upstream.  So you buy another vacuum
actuator ("motor") and be done with it.

Good luck.
Divide and conquer; classic t/s.