We have all been there, a stuck and stripped bolt. Especially if you have a boat this can be particularly painful as decades of salt and metal galvanic corrosion really work together to ruin you day. In my case we had four through screws stuck inside the power control of the binnacle.
The hope came when I found this (Irwin reference for metal drilling) in that rpm and feeding speed are crucial to success vs. psychotic episodes! I definitely recommend it, good read.