Get a left handed drill bit . They sell them at auto stores. Sears has a kit based on this same principle. Used your reversible drill on reverse.Drill slow and add a drop or two of oil. Once the drill catches 9 times out of 10 the screw or bolt will back right out. If that doesn't work use a regular drill the root size of the bolt or screw. Root being the size less the threads. Chase the threads with a thread chaser or tap and you're done. I break a lot of bolts. The hardest part is not to panic and rush. The more careful you are the quicker you're done. Good luck.
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