hi, i had some exhaust studs snap off like yours, but was a bit luckier with the drill. While extracting one of mine i ended up drilling way off centre, but still manged to get it out. can you drill another hole off centre, you say the stud was loose. Just use a nut or similar as a guide(and vise grips to hold nut) to keep from drilling into head. From memory I used an extractor of about 3.5mm dia, i cant remember the brand (but not one with a thread, just parallel ribs running the length of it, someone mentioned the brand on another post), an excellent product!. Other than that i can only think your solution is best.
P.S. I replaced all the studs at the same time, another couple of them decided to break during that process, which was in one way lucky cause its not a job you want to do twice!