NO HAND DRILL!
You have probably already done this - it's a long shot but by chance, have you removed the base to see how much of the screw is left sticking up? I have had cheap heads come off the screws and removed the base to find enough of the screw to remove with vise grips.
That might be worth a try. Personally I think he's xcrewed.
SS screw snapped??? You've gotta think the screw was glued (locktite) in or somehow welded/rusted tight from firing. I'd try lubricating and or heating the screw first before trying to rotate it back and forth...just to get it loose. Once you get it to "move" just a little, you might be able to gradually work it out?!
Drilling thru SS you would need special diamond tipped bits (something harder than SS) to either drill the hole out completley or enough to be able to get a screw extractor to bite and hold. (heat and lubrication) (locked in a vise and variable speed drill press, one that doesn't wobble preferably)
I'd bet he.d be lucky to find one gunsmith in his state that wouldn't botch the job.
If that screw won't budge, might be better of grinding, sanding, polishing flat and look to drill and tap in another location.
I've got a similar problem, two screws on my scope base (hex head) will absolutely not move. Fact is I'm starting to strip one hex and I.ve stopped before I completley eff it up. The other hex screw I snapped an Allen wrench !!! trying to turn it out!!! Whoever mounted this base, sure didn't want it to move? WTF