I've drill 3 now, drill press, very careful, very slow, very stressful!
What size bit, and HSS? Cobalt? TiN? I've gotten things like that out before. If it just broke through and grabbed/ twisted off my first remedy would be to cut a piece of HSS drillrod of the next size down and carefully try to tap it through the rest of the way. If it's HSS that's broken off, cobalt will drill through but need to be set up very stable in the press and minimum bit sticking out of the chuck. Could drill slightly oversized with a small solid carbide end mill, punch out broken bit, clean up hole and use adjustable gas block. And pictures!