I took a look at the spare Gen I (1995) dash I have, and it looks like the glove box door pivots are using expanding push-type fasteners. You might try carefully prying the center piece of the black pivot point out about 1/8 to 1/4 inch, then seeing if you can pull the whole plastic piece (both inner and outer) out at the same time.
If thats not do-able, then I'd try removing the passenger knee panel (just a few easily-visible screws), and I beleive you can see the back-side of the pivots there.
And, if not...
Removing the dash is very easy - carefully pull the bezel around the A/C and stereo head unit controls, remove the screws holding both knee panels in place, reach on top of the headlight switch body (behind the dash) and press the button you can feel and pull the headlight knob and shaft out, remove the screws across the bottom of the dash and on either side of the stereo, and carefully pry the top edge away of the gray dash away from the black rear dash. Only hard part is getting the dash up and from behind the steering wheel.