Mickey,
Here's a tip that's worked VERY well for me, using a hex bit for a powered driver, use one of those rechargeable impact drivers and put some weight on it and give the trigger a little 'burp' in the stuck screw. I've fought with some base screws in the past and one day I noticed my impact gun sitting there from a little construction project... It works as slick as anything I've ever tried and the screws will back right out. I've drilled off enough screw heads to know what a pain it can be, but this really works!
