OK, stuff like this kills my brain! lol So, you've tried the 1,2,3 pull from the outside, but I think the door is going to require more of an abrupt shock. I would study the other door, and its workings, and make sure the bad door mechanisms are doing the door opening, like when you push the button, the rod going to the latch is "unlatching", and the thumb lock is definitely all the way up(you already said you did, but have to recheck)! My passenger door with the slightest bump the thumblock falls downward and locks itself. Then knowing you've sprayed and soaked the latch thoroughly, and maybe even tapping on the latch from the inside of the door. This is your only access to the latch at this time, right?
Here's my idea: you don't have to do it, but it's just an idea mind you and don't laugh! lol
I'd take a piece of wood, eh, 2 x 4(there's no exact science to this), place it as close to the latch side of the door, the meatiest part of the door, from inside the car (have someone hold it or tie it up. The large area will allow more surface area to be absorbed by the door, so not to damage it(hopefully).
Ok, here's the clincher!
take a 4 x 4 about 3' long, your battering ram so to speak. Like when the vikings are trying to break down the door to the castle. ( A large heavy hammer would probably work too) Someone has to push the botton and hold it down. The wood(the target) would have to be tight against the door I would certainly think. Seats are forward, and the passenger side door open to allow a moderate swing(if using a battering ram. So, now, boom boom boom! kind of tease ramming the door from the inside of the car and see what happens.
CAUTION: there is a problem with this idea! the glass could probably shatter! Maybe taping it with duct tape would help prevent. When these windows go, they shatter into tiny pieces(safety glass).
I'm alone, and just set up a mock type for demonstration.
http://img.photobucket.com/albums/v4...e/IMG_8067.jpg
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My second thought, or 1st thought, was to take a portapower, and use it from the inside of the mustang, pushing from the pillar on the opposite side of the bad door, use the 2x4 as above, and put pressue on with the portapower, but just enough so not to bend the door.
Right now, that's about all I got to offer, but I'm still percolating on this problem.
If you'd like to talk, call me, dne', 832-607-9116 and talk it with what ideas you have, etc.
dne'
71 DS door won't open - help! 
. is the door closed or open? The sentence below that you wrote; Now is the door open so that you can get to the screws? are you referring to the door latch screws(3 of em)? If the door is open and you do have access, you have a couple options: use a hand impact with a phillips head attachment, or drill them out. But if your door is closed, I'm certain it would be impossible to get to the screws! So, when these questions are answered, then I can think better on what's actually going on. 
Be specific cause the reader needs to know details.
. Why or why they didn't just use hexheads is beyond me.
