Have you ever have one of those (fill in the blank) kind of days? The screw problem was just 1 issue. After having detailed my wife's car, It caught an eagle sized bird bomb. Get this, it hit the roof line just above the drivers door. This bird must have been moving because when I went to the car to wash it off, I noticed the
passenger seat and door panel was splattered with white bombs in shotgun pattern

Yep, the driver's window was open. Michael Jordan couln't have made that shot!
Back to the screw. I'll go back to the 1/8" drill and go deeper, and expand in smaller increments. I think going up to 1/4 was just to big a jump and hence I ruined the bit. Once I can use 1/4" I'll in efect have seperated the head form the shaft and then be able to work the threaded section out. The embarrasing part is, is that is not a big screw (threaded section is only about 1/8" thick).
I have 5 different extractors, but because the mounting surface for the screw will move when hammered, I'm not sure they'll bet the necessary bite.
Because of the tight location & proximity to delicate surfaces, an impact gun won't work with this application.
Thanx so much for the replies and sound advise. Hopefully I don't have another "one of those days" for a while!