Mike, as Roger said, use the socket drive pozi-driver. Also use an extension on the socket to get your knuckles away from the door and dash etc. loosen just enough to move the door hinge alittle at a time. If you just want to bring the top hinge side door edge out a hair, just try to loosen the top hinge screws just a smidgen. Sometimes that is all you will need. Hopefully the rear edge will fall into place for you. If not you'll have to keep playing with it till all seems right.
Just as a matter of comment, since I have just about completed the complete reconstruction of my Healey body, I found that I needed just one shim on the upper door hinge of the right side door to get the seams and gaps as I wanted them. I was a bit disappointed that I needed to use any shim at all given the amount of panel work that I did on this car. the reason I was disappointed was that on disassembly of the car I noticed that there were absolutely no shims use previously. I know that my car was a realatively unmolested car before I got it an wondered if it might have been assembled that way at the factory. I find it curious that it might have been put together that way (without shims) at the factory given their production tolerances at the time. Having said that, prior to my disassembly, the seams were not all that great.