OK, so here's what I'm dealing with at the moment on a snowblower that I'm working on:

The muffler bolt broke off upon removal, but there wasn't enough left to grab on and remove so I ground it down flat, center punched, and drilled it out. I picked out all the small bits, but there was still some left in the threads so I started tapping it. Well, I got impatient and pushed the tap a bit too much and this is what happened.
The hole is 75% open on the back side, because one of the cooling fins partially blocks it, so my only real option is to try to get the tap out the way it went in.
I'm open to all suggestions, but keep in mind it's mounted to a 200lb snowblower so taking it anywhere but my garage is probably not an option.
Does anyone have one of these, or at least successfully used one in the past?
http://www.waltontools.com/products/extract-machsc-hand.htm
I can buy one if I know that it will work. The broken tap is a 5/16 - 18 4 flute, and it was from an old Craftsman set, so it's very good quality HSS material and not just a basic carbon steel bit.
Thanks in advance.

The muffler bolt broke off upon removal, but there wasn't enough left to grab on and remove so I ground it down flat, center punched, and drilled it out. I picked out all the small bits, but there was still some left in the threads so I started tapping it. Well, I got impatient and pushed the tap a bit too much and this is what happened.
The hole is 75% open on the back side, because one of the cooling fins partially blocks it, so my only real option is to try to get the tap out the way it went in.
I'm open to all suggestions, but keep in mind it's mounted to a 200lb snowblower so taking it anywhere but my garage is probably not an option.
Does anyone have one of these, or at least successfully used one in the past?
http://www.waltontools.com/products/extract-machsc-hand.htm
I can buy one if I know that it will work. The broken tap is a 5/16 - 18 4 flute, and it was from an old Craftsman set, so it's very good quality HSS material and not just a basic carbon steel bit.
Thanks in advance.