Also, [probably too late now, if you started the drilling] another way is to cut in a 'screwdriver slot' with a Dremel tool and then use a hand held[ hit with hammer type] imnpact driver on that..
I have used that method with some sucess also.. works well if it's broken off flush, or just above flush..

 

Interesting idea. I like that.

 

Have you tried heating it up with a torch?

 

Dont have a torch. but I like that idea with the Dremel making a flat head end on it. I may see if I can get that to work. We'll see tomorrow if I have time.

 

Duct tape, it'll fix anything....

 

If you can use the dremel to make a flathead slot deep enough, use a 3/8" flathead socket, and an adapter with a 1/2" drive ratchet and a breaker bar. Should do the trick.

 

I prefer the hand held impact driver[ like 10 bux most places[or less] as it pushes IN and turns it[less likely to strip the slot out]works often tho really..