Chances are and this is from experience the carbide cutter will be toast when you are done if you get done.
How much is a new one of them ? Then if you don't get every last bit out you either snap or usually blunt the next tap down the hole – more expense.
Doing this for a living on equipment where expense is no problem it still gets expensive.
Now many are not going to like this as being too rough but it works, it's quick and it's cheap. Plus it works every time.
Take an angle grinder with a thin cutting disk, attack the job from the best side travelling the way of the tap, when you have a slot remove everything even it it means widening the slot, then weld up, mill or file back to shape, drill and re-tap.
Don't quench at any point, allow to cool naturally and you won't get any hard spots.
Edited By John Stevenson on 04/02/2014 19:08:55