Well, the answer to your question is, remove the screws and the door at the same time. Then you can wiggle the top screw out.
Your door is likely not sitting straight, and the screws you are referring to are the ones in the trailer side of the hinge. I took the door off, but kept the hinges on the door. Then I filled in the holes that the screws were in with fibreglass and resin. Just before the resin hardened, I used a boxing knife to scrape the excess resin off the trailer, and trim the fibreglass that was hanging out of the hole, so it was flush with the side of the trailer. Then, I used boxing tape to put the door in the hole where it looked right, so the gap all the way around the door was the same. It took me three tries to get it right.
I had purchased new stainless steel screws that were the same length as the originals. I drilled holes that allowed the screws to bite a bit, but not too much. I gently worked the screws slowly in and out of the holes, a few turns in, then back out till I had them seated. Then I filled the newly drilled holes with fibreglass and resin again. But while the resin was still liquid I screwed the screws in, and waited for the resin to harden.
Since the holes in the door were not so bad, I just bought very similar stainless steel screws. Removed one of the three in each hinge, and filled the hole with resin and glass, then screwed the new screw in and waited for the resin to harden. Repeat two more times, till you have replaced all the screws in the door.
Bob's your uncle. Good as new and ready for another 30 years. There was a bit of clean up, but that is basically it.
Oh yah, that difficult to remove screw will also have to be in the hinge, when you re-install it.