Short of sending it to Sean, I would use a left handed twist drill but there is a huge caveat. I would only do this if you were certain the pilot hole that is already drilled is centered and straight. If it is angled to a side, you will not have far to go before getting into the carb body threads. You also cannot drill deeply either.
I'd prefer the carb off and using a drill press and a collar stop on the bit. Of course start out with as small a bit as possible and get wide as you dare. My experience has been that the screw gets so thin the heat is what is releasing or breaking the screw loose. If in doubt, send it to Sean. There is no gaurantee he will be successful either but I doubt he charges you anything is he can't get it out, plus he can sell you the new screw, spring and o ring not to mention, why not have the best brain surgeon operating. Do I need say what a replacement carb body costs!
Good luck either way.