Maybe an easier approach would be cutting away the broken off screws, Ernst.
There are some small hole saws for use in drills or die grinders with 1/4"
collets that could be used to cut out the base metal around the frozen
I saw some yesterday that had diamond grit on them, but carbon steel saw
teeth or carbide grit would likely be better.
Another method would be to use a piece of tubing in a drill chuck and dip it
in a grit paste like valve grinding compound. May get a bit messy, but a
good solvent on a rag should be all that's required for cleanup, just avoid
too much rubbing.
I think you mentioned the screws were in a window frame of some sort. If
there is a feature (channel or edge) that would position a guide over the
screw stub (so the hole saw can't run away), make up a guide for a small
hole saw that could be clamped into position for cutting out a broken screw,
then repositioned over another, etc.
It shouldn't be too difficult to find something to fill the hole (push-in
plastic gizzy, etc) for a new screw to anchor in.. or just fill the holes
with some "miracle hole filler in a tube" and screw into that.
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