Those studs are very hard. Normally i drill 1/4-1/2 into the stud. there has been times i had to drill the whole thing out and re-thread it.
All i can add is, best of luck and
http://www.plymouthlaser.com/tbolt.htm. I had to do this on my 7cm housing, if you can, go all the way. I even took it to a little mom and pop machine shop and he handed it back to me, "it keeps breaking my drill bits, i cant do, so sorry"
Took some heavy machinery at a brewing company (will leave nameless) machine shop to get the bolt out.
If your drill bit is harder than the material you are cutting, you'll do fine. If its a cheap bit and softer than the bolt/stud, dont bother. If you are at 1/4", hammer in the extractor then give it a go.
Here is me working on a broken bolt. Softer than your stud, but same principal.
http://www.youtube.com/watch?v=u8wspxPKWLA
This was also informative if you have the tools.
http://www.youtube.com/watch?v=cTRUXRv2HFs