when I ws repairing antiques, I purchased every "broken screw removal " tool I could find. They were all inadequate in one aspect or another.
The panacea I found was a split roll pin, which are available in many sizes inexpensively.
A quik dremel cut off wheel turned the edge of the "split" square, to resemble the edges of a plug cutter.
You choose one slightly less that the diameter of the screw threads, chuck it in a drill and run it backwards
What happens, as you cut down, the heat of the friction, and the friction eventually causes the e broken bit to just pop up.
I know I've posted video on this before, but long ago and cannot find the link....tie to do it again.