Do you own an air chisel? You could fold the pipe in on itself quite easily with that...
Here's something I successfully tried once to extract a broken pipe nipple-
First, I suggest soaking around the nipple with WD-40 or other penetrant for a day or two. Then-
1) Cut a rectangle of steel plate with a slight taper down it's length so that it will *mostly* fit all the way into the broken nipple by hand, and long enough that an inch still sticks out (enough to grab well with vise grips
2) Using a thin cutoff wheel in an angle grinder, or a hacksaw or file, cut a shallow groove down each long side of the steel plate so that when inserted into the pipe, the edges on each side of this groove will bite into the pipe.
3) Put 2" of the baddest, blackest, used engine oil you have into a metal pot or pan, and ready a fire extinguisher just in case
3) Grabbing the extractor you just formed in a pair of vise grips, put the torch to it, getting is as hot as you can- cherry red, especially the edges.
4) Immediately quench in the used motor oil. This draws carbon from the oil into the outer layer of the steel, "case hardening" it.
5) Once cool, repeat a few times. It will be left with a nice, attractive black finish, even after wiping it off.
6) After repeated hardening and cooling, insert your new extractor into the pipe, and give it a couple of whacks with a hammer. This is where the taper and grooves (or flutes) come in. It should bite into the pipe, and sit down lower than it would fit by hand. If you put one edge of the extractor beside the pipe's welded seam, that gives it an even better bite.
7) Clamp on your vise grips, and unscrew the dang thing!