I'd forget the 'easy out'. You might want to try drilling it out with a slightly smaller L.H. drill bit (in a reversible drill of course). The offending screw will often 'back itself out' while doing so. Just be sure that the L.H. bit is nice and sharp (and of a good quality). I've removed more than a few badly stuck/broken bolts using this method (mostly exhaust manifold bolts).
