The gunsmith got it out. He said it was the first one he'd ever seen break.

I did not, however, asked how he did it. I was too relieved that it actually did come out. He also tried to give me the remainder of the snake, which was about 10 inches long (the barrel was 16", to give an idea of how much it was stretched). It actually broke just before the end of the brass brush portion, as he said that he was pulling out little pieces of brass (seems like he pulled it through). I thought I had all of the brush out, but I guess not.

The rifle is back together now, and is working fine.

The lesson I've learned:

I'm no longer using boresnakes on my long guns. I'll still use them for pistols though (as someone said that would be easier to fix). If I ever do use them for rifles again, I'll be sure to attach a piece of parachute cord to the back so that I can pull it back through if necessary.