Patching and Plastering - curtain bracket screws won't budge

I just purchased a home where the previous owner loved traverse rods, and I removed the one in the living room that spanned a beautiful bay window. The rod came down just fine, but I have four brackets that were installed into studs. They were installed well, as evidenced by the fact that I now can't get them out (they've probably been there over twenty years). The drill doesn't to the job, and I've tried manually with a large screw driver, but I just can't get the flat screw heads to budge (the screwdriver keeps slipping off the screw head). Any suggestions for how to get the screws out?

Can you heat it without burning anything?

Put the screwdriver on the head and hit it with a hammer. Sometimes, it will losen it.

Try to move it by tightening it.

Reverse drill bits.

Easy outs.