The compressor should be the 6C17 on this car... it's a variable displacement unit that should not cycle. Anytime the outside temperature is warmer than a few degrees above freezing, the compressor should be always be engaged with the ATC on. The fact that it cycles suggests a problem. This system is hard to service unless one knows exactly what one's doing. That compressor doesn't like anything but R12. It can be made to work with other refrigerants, but it'll make you jump through some hoops first.
As for the blend door, I'd run the ATC self test and see if it throws a code first. Press and hold auto, floor, and defrost until the display starts flashing. It'll run the test and show codes in the display. If it does, press the panel button to continue testing (this part has never worked for me though). Otherwise, the blend door servo is under the airbox by the accellerator pedal.
While you're at it, maybe check that your aspirator fan is working... it's located behind the instrument cluster. These love to fail. Any 1988-1993 ATC equipped car at the salvage yard can give you a replacement. The Imperial has one from a 1988 New Yorker in it. You should be able to hear it working faintly if you turn the ignition to the run position without starting the engine and turn off the ATC.