put a dab of superglue on the tip of your screwdriver and superglue it to the tip of the screw lightly twist screw till it comes out dip tip of screwdriver and screw in nail polish with acyton in it to disolve the super glue hope it helps you works 99% of the time for me
That epic failed for me, but here's my way:
Have a minion (brother, sister, mom, etc.) hold any screwdriver you're willing to waste onto the screw. Heat the tip of the screwdriver with your soldering iron. Then, apply a couple dabs of solder. Remove iron, let cool, twist, and remove!!