My favorite and most successful broken screw removal method is using the TIG welder.
Weld a little blob on top of whatever is left and grab that with vice grips. If a hard to get spot use a nut or bolt welded to it.

If you want to bring it by I'll give it a try.

Grigg

•1951 GMC 250 in the Project Journals
•1948 Chevrolet 6400 - Detroit Diesel 4-53T - Roadranger 10 speed overdrive - 4 wheel disc brakes
•1952 Chevrolet 3800 pickup
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"First, get a clear notion of what you desire to accomplish, and then in all probability you will succeed in doing it..." -Henry Maudslay-