Those screws aren't super tight (normally), so if no screwdriver is going to work, I'd try getting a small but relatively sharp chisel, and using that and a small hammer, tap the screw with the chisel in a counter-clockwise fashion until you get it out. Although, looking at the picture, if you try a couple other screwdrivers, perhaps you can get one that sits in there perfectly.
Or, you can drill the head of the screw off and not run a screw there. If the rest of the door panel screws are in place, you won't miss that one. My old G didn't have the screw in there anymore.
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