With an Allen head you have great advantage...the hex will nicely center a drill bit. Go to largest bit that will enter the hex, run it through being careful to stay perpendicular.
From here move up one size at a time, letting drill slowly follow the pilot hole until you reach a size where you see the threads just beginning to appear. Then, you attack with a dental pick and shell out the remaing shreds til hole will accept a tap and a new screw.
EZ outs are more dangerous than useful...small ones are very brittle, and if screw is truly stuck and the and the EZ actually grips well, it is going to snap. You then have a hole full of metal that is harder than your drillbit.