IF you are going to the hassle of drilling, don't use an ordinary right hand drill bit. Get a left hand bit. Set your drill to "R". Get it well centered. What will happen - at worst you will drill a hole in the remaining stud, which you can get out*.....or best the stud will unscrew with the drilling.
Of course the bit should be smaller than the stud.
* I have NEVER in my 35 years of wrenching never had luck with easy outs and their like. They are just too brittle. They break in the hole and you are screwed....well not entirely - next comes my secret weapon. Diamond tipped bits for the Dremel type tool. Once you have a hole drilled, or an easy out broken, or in a real pinch, just get 4 or 5 (maybe 2) ball shaped bits, and carefully go for it. Takes a little time. But has never failed me.