Spark,
I do a lot of rewires on old houses. One thing I learned early on was to order the Type"M" masonary flex bits for walls with plaster where the plaster is piled up as much as a foot thick on top of the firestops and bracing.
You can sharpen the wood bits but you might as well grind off the screw point first. If you use a drill doctor you need two people or else lean the end against a wall.
I wonder how hard it would be to cut the old bit off and weld a new one onto the rod?
Brian