I've had luck with carbide drills to remove broken taps and then make a press fit plug and redrilled. First use a carbide burr with a flat or round bottom to get a flat surface or better yet a contoured surface. The contour will center the drill to reduce breakage or bending. Most small carbide drills are cheapish. I bought two for a hardened threading job, and later found they saved my hide a couple times over in the tapping, drilling area. With your job being drill bits I'm not sure how it would react to the flutes or try to follow them just trying to get the bit out. But if you are planning a plug job, I would buy one at the plug size , and will most likely just drill right thru easily, also having a larger point, the flutes of the broken bit would become negligible.