I know your pain! I had this happen to me when I changed the front shock last month. ...only I had both lower bolts break on the driver's side. I grabbed my Craftsman extractors and no luck. The problem is that no drill has the power to remove corroded bolts. Think about it, why did they break in the first place???
So I grabbed my drill punch, drill, sharp titanium drill bits, 8mm x 1.25 tap and cutting oil. The key is to use the drill punch on the broken shaft so as to make it easier to keep your drill bit centered. Once you punched enough to make an indent, grab a small bit (1/8) and drill (straight up through the stud. Once you're through, grab a bigger bit to widen out the hole. ...after every time you go up a bit sized look at the hole that you drilled. Once you see faint thread marks on the sides, you can grab an ice pick to chip away some of the starter threads. ...either on the top or bottom, whichever is easier. Once you've chipped out some of that first course of thread, grab the tap and slather it with cutting oil. Remember that once you get it started, for every half turn you make back it all of the way out so as to clear the debris. If you take your time and check the sides after each drilling you'll get it out. Good luck!!!