What I'd do to get a punch right in the centre is to grind the broken stud level, Then, leaving the drive shaft in place, put the cover back on with the 3 remaining screws. Then use a 'transfer punch' to punch the broken screw.... That should make a very well centred punch mark, and starting point for the extraction process.
Also, not a fan of 'easi-outs'. Their problem is that as they screw in, they actually spread the screw you're trying to remove, making it tighter. I prefer to just heat it up nice and hot, a few times. The reason it broke was that water has gotten into the threads and started the corrosion process. Heating it up will drive the water out and allow the screw to turn with a lot less torque. I'd drill and tap a smaller hole and use a high tensile bolt. Loctite it in with red locitite, then wait overnight, next morning, unscrew the stud.
BTW, don't get bulldozed into paying that extra hour. In that position, no excuse for breaking that screw off. That tech was being 'ham-fisted'... He would absolutely have known it was too tight. He should have stopped and hit it with a)heat, and b) a hammer (helps break the bond of the corrosion. Done it plenty of times myself)....
Chris.......