I was in my local hardware today and asked about left hand drills. He said we don't carry them but we do have a screw extractor with a built in left hand drill. I bought 1/4" or Metric 6. You grind flat, punch the center and drill counter clock wise when the hole is deep enough the extractor bites into the side and if all is right and holy the bolt comes out. I haven't needed to try it but some sunday evening when every thing is closed I sure will need it.
They had ones for 1/4, 5/16, 3/8 and 1/2 inch bolts.
It is the Alden Corporation Walcott CT 06716
The name is DRILL-OUT Power Extractor