Tough Windshield Clip Screws

On my 74 Dart Sport, I have the windshield out, and I'm trying to remove the trim clip screws.

Some of the heads are rusted (nothing to put the screwdriver in), so I tried drilling them. Wow! They are tough. I'm using new bits. Some were weak enough that they popped with a bit of chiseling. Two, I was able to get vise grips on them. A few drilled, and weren't too tough. They're not spinning. I have two extra stubborn ones left. I can't chisel and hammer too much, I've bent the window channel in a couple spots.

I'm slowing getting them, but what makes them so hard to drill?