I believe you can still buy new latches (were available last year).
Brenda's Cougar did the same thing really bad, we just lubricated it. What you described sounds like exactly what her car was doing, kept having to flip the thing up. I bought two latches, and they are still sitting on the shelf because I realized how hard the job was!
There are like four rods attached to the latch, and the whole R&R is done with two fingers. Oh, did I mention you cannot see in that corner of the door cavity where you are working. That is why they are still sitting on the shelf!
Removing one from the junkyard is the way to go cause you can "practice" on that car.
Good luck with it.
97 T-Bird LX 4.6 - 80k miles
94 Supra TT Auto - street/strip car
04 CVPI- Brenda's car - 76k miles
95 T-Bird LX 4.6 - fully optioned, owned 15 years, 220k miles
96 Cougar XR-7 4.6- Brenda's car, owned 11 years, 187k miles
88 T-Bird 3.8 - first T-Bird, owned 5 years, 206k miles