Jim,
Use the Snap-On collet type stud extractor for this job. Cut 10mm threads on the end of the remaining head stud, thread the extractor on and TIGHTEN, then extract. Easier said than done, but this method worked like a champ for us with 2 similar broken studs. If it still dosent want to budge, heat the inside of the case where the stud is threaded to melt the factory loctite.
EDIT: Sorry, just read only 1/4" inch remaining.....you sure that's all you have to work with?
