Steve,
Split end for end or did you just leave the neck in the chamber?
My first thought is a GI broken shell extractor. Chamber it and when the bolt's extractor starts to pull the broken shell extractor back out, the end expands outward to catch the mouth of the ctg.
Another way is to take a piece of brass rod (steel rod would score the bore or chamber), split the ends and spread them out like a cotter pin. Not too much; you need to be able to squeeze the ends back together enough to get the rod started into the muzzle. Tapping the end should cause the split ends to grab and push the broken shell out of the chamber. May take several tries but then what else do you have to do with your day?
As a last resort; get rid of the head of the cartridge if it's not already gone and go after it with a chamber reamer. The reamer will cut out the brass and by taking it slow, you'll know when it's completely cleaned up the chamber.