TIG weld something on the end of the screw enough to grab it with vice grips and often effortlessly remove them.

the welding heats the screw and the thought is that it expands in the hole and crushes the rust some, making it a little freer and easier to remove.

All I can say it is works 98% of the time, I've removed hundreds of broken fasteners with this method, and can only think of a couple where it hasn't worked.

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-