After cleaning it the way everyone said, I was running a big dry cloth down it and the piece broke off of my cleaning rod and the patch and broken rod end is stuck down at the bottom. Took it to a gunsmith and after trying to pull it out with a claw for 10 minutes, he said "shoot it out." Anyone ever tried this?

You can shoot them out if you want. Have you tried an air compressor? Sometimes if you remove the nipple you can put an air compressor there and some short bursts of air will pop that out without shooting it out.

Other wise, take the bolster clean out screw out if you have one and it will come out, or the nipple will work also. Then pour as much powder into it as you can get. I use a nipple pick to pack it in there. When you got it well packed, then replace the nipple. Next you need to push that jag and patch as far down as possible. Then cap it and take it outside and shoot it out. Point it at the ground. The last time I did this, it shot the jag four inches into the ground, so there is some power here.

I had the same problem with a cleaning brush. Here's what a gunsmith told me. If your patch won't hold back enough gas to clear the barrel, take out the nipple/ touch hole. Heat bee's wax( not parafin, it cools to quick) Run a swab up the barrel to the obstruction and let it there. Pour enough wax into the touch hole to form a plug( leave enough room for powder) Let it cool, remove the swab, work powder into the touch hole, and fire the plug out. Make sure there isn't any extra room between the powder and the plug or it'll act like a ball that's not seated. It worked great for me.

I've shot them out. Like cayugad said, point it at the ground, it's got some power behind it.