I have a 1982 Trek 730 with broken off drop out screws.
WNG on the Classic & Vintage forum has suggested soaking them with penetrating oil and then have someone tack-weld a small screwdriver to the ends and see if they can be screwed out.
I've thought of maybe using a fine file to cut screw slots into the ends, being very careful to not damage the drop out threads, and then trying to screw them out. My Dawes Altantis had the same problem but the screws had screw slots on the inner ends and they screwed out v. easily.
Does anyone have any other tricks they have tried with success, or think would work?
I suggested to my bike mechanic using a fine drill to drill hole in the ends and then insert something to screw them out but he reckoned I would risk splitting the drop out.