I would suggest you are better off having two switches (opto, magnetic, or even mechanical) that detect door fully closed and fully open conditons, that way your program can command the servo to stop without having to worry about stalled condition, or having to determine exact timing of travel.
Hmm, there goes another I/O pin or 2!
I was hoping a stalled condition wouldn't be too hard on a servo...
perhaps Sparkfun's Optical Detector / Phototransistor - QRD1114
could detect 2 end marks or protrusions added to the side of the drawer to give the right span.