Ever break a drill bit down a drilled hole. If so you will know it is a PITA to remove, well here is what I made when I could not remove the broken piece deep in the hole.
First I ground one half of the spiral and then ground remaining to fit between the broken bit and the wall of the hole. To use, twist into the hole and through the broken bit. Pull down with a pair of vice grips.
I hope it works well for you as it did from me.