Broken tub faucet drain inside wall

I have a pickle here. I'm replacing the tub faucet on an older home (50s), and when I removed the tub faucet, the pipe broke off. Problem is, it's a steel pipe and the the threaded part is about 2.5 inches behind the tile. Since it's steel, it's horribly corroded on the inside and a nipple extractor can't grab it...plus it's too far in the wall.

I was able to hacksaw enough of it to get most off it out of the way, up to the point where it's threaded. I can't saw any deeper or I'll cut into the brass threads. Is there any options here besides tearing into the wall to get the rest of this out of the brass valve body, or do I have to replace the valve body?

I can access it from the back, sorta. I would have to cut the drywall behind a toilet in my 2nd bath. Not ideal, but It's an option.

 

Is there an easy-out that is long enough to get that far back into the wall? The ones I have are fairly short.

 

A twelve-point socket on an extension should be allow you to go pretty much as deep as you want to go. That's one reason why galvanized nipples or other bits should NEVER be used with potable water. The galvanization only slows down the thing from rusting, and the cut end and threads usually don't have any protection at all.