The bolt that holds my rear rack and fenders broke off flush with the frame. I picked up a bolt extractor and could not get the portion of the bolt out of the frame. So, now I have a hole drilled all the way through what is left of the bolt.

I'm afraid to keep going to a bigger drill bit, since I'll eventually be drilling and damaging the frame.

So, here are my two thoughts on where to go from here:

First option is to pick up a left-handed extraction bit. I don't have to back the remainder of bolt out of the frame. With a backward extraction bit, I would just drive the bolt on out the other side.

Second is that I get a tap/die set and just rethread the mounting hole. If I don't hit it dead center, it will rethread the frame on one side and the remainder of the broken bolt on the other. Once I have a new bolt screwed in, everything would get locked into place and I'd never have to worry about it again.

Any other thoughts on how I can get my rack back onto my bike?