I would drill elsewhere, finding a decent place for screws to fix and then fill in old and new holes.
I previously tried driving in a 75mm drywall screen just beneath one of the existing screws. I drove it in straight/perpendicular, not at an angle, and it never bit. There's clearly just a void directly behind these screws.From the photos, it kinda looks like you have plasterboard over a moisture resistant backing (maybe).
I would expect that there is a timber stud running along the wall. I have no idea why the screws are at an angle.
I suspect that the problems are the result of the screws being buried to too deep.
Try drilling above or below the screws holes and see if you can get a decent fitting.
Standard plasterboard is 9.5+mm the backing might 18(?)mm. If so, a 50mm plasterboard screw might suffice.
Could it be that the stud somehow sits in the corner of the wall (remember - this is a dormer) and that is why the plasterer used very long screws and driven them at an angle?
If so, I'm not quite sure what to do. I could, of course, just fill the holes and hope the screw pops don't come back! But ideally I'd like to understand the issue clearly.
