I use an industrial grade screw gun. Not a drywall gun, but similar. They have an adjustable clutch, finely divided 0 to 100% grab, which is heavily influenced on how hard you push into the fastener, and how hard you squeeze the trigger. Since I started using it for getting out stubborn screws, I have had an absolutely 100% success removing screws - and all with absolutely zero damage! Some things (like tiny instrument face plate screws) don't like being smacked with a hammer, and this tool works especially well for delicate screws. These things are NOT intended for this, but I can not overstate how superbly they work for this task. They are very expensive, but worth it at least to me. The Black and Decker's are no longer available, which is why I show the rusty DeWalt, which can still be found new, which is of similar design and works well. The B&D's were made in three grades: Heavy Duty?, Professional, and Industrial. Industrial is what you want. See one in a flea market, get it! These things are a lifetime tool. I still have a few from commercial work, which is how they are so beat up, but I bet the one in the pic has had at least 4 trigger switches and 10 cords, and still kicks ass!