That happened to my 1993 Navigator, which I believe is identical to yours. I eventually got it open without damaging the door or the door frame, but I've forgotten just exactly what I did. I think I opened the door to the next compartment and used a screwdriver to push the latch back.
Since it is the air condition compartment, you can go from under the coach where the compartment is vented. You should be able to access the latch from under that compartment going to the right of the air conditioning unit. (I built extra sewer hose storage here, so I know there is some room.)
Holiday Rambler Navigator DP, Hummer, and Honda VT1100C Shadow