Sure hope you have a good outcome to this problem. As a retired machinest, I have removed more broken bolts than I care to remember. I have always said there is no better teacher than pain, and we learn quickly when it hurts bad. Long ago I learned when removing broken bolts, ALL efforts have to be in line with the centerline of the bolt. If drilling a hole for a easy- out, you absolutely must be drilling in the bolt center. Close to center is NOT good enough!!! If off center, the easy-out will not turn concentric to the bolt, most likely resulting in the easy-out breaking. Then things are really complicated, because the easy-out is hardened. Broken drill bits are caused by using a dull bit, misalignment, trying to go too fast, and not pulling bit from hole frequently and blowing hole out with compressed air. Use oil on the drill bit! To maintain alignment, take a short bolt of the same size to a machinest with a lathe, and have a hole drilled thru it on center, the same diameter you want in the broken bolt. Screw this guide in above the broken bolt if possible. To start drilling, use a center drill. They are more rigid and less likely to walk off center. Go slow, drilling with a pecking action and light pressure to start. Hopefully these tips will help keep some out of trouble, but are not everything needed to know on the subject. Above all, do not get in a hurry, and DO NOT get off center. Ask questions.