I had a long drawn out battle with a screw that welded itself to the grab handle. There are no good extractors for really stuck screws. I did find a dremel bit that was the bomb. After trying every drill bit known to man.
If you still need something to drill out a screw let me know and I’ll find the info. Although it looks like you have a different problem. After I got the head off mine it twisted right out. Maybe a reverse drill bit might work.
For what you have there I would bed it in butyl tape. You can clean it up and caulk the edges so it looks nice. The problem is getting a good seal on the irregular areas. Butyl is easier to maintain and clean up if you need to take it apart again.