use an impact driver! Seriously. It will make short work of it and save the screw head.

I had a self tacker jib track from a Nacra 20 where the end of the traveler track was ripped off during a backwards pitchpole in surf (a half-gainer-pole?). The track was attached with stainless machine screws into a thick aluminum bar but the aluminum bar didn't even appear to be tapped. It looked like they just got the holes close and drove the screws into them. With absolutely no barrier between the metals, they corroded badly. I spent a month tinkering with that thing and no penetrating fluid or anything I tried would budge any of those phillips flat head screws so I shoved it on a shelf and forgot about it. Sometime later, I bought a Ridgid tool set that included an impact driver and after being pretty impressed with that thing, I came across that traveler track and I wondered how it would do. The verdict? Amazing. Every screw came out with almost no effort using the impact driver. To make sure I hadn't lost my mind, I tried a couple with a manual screw driver and had the same result - couldn't budge the screw and started to destroy the head. The impact driver immediately removed the screw right after that.

This thing has become one of my favorite tools.