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It almost sounds like the barrel has an obstruction in it due to leading. That is, lead has been shaved off the bullet when it is travelling through the bore. Many times a rough spot in the bore due to rust or build up of unburned powder, or some other cause will cause this.
First of all, I would try some of the foaming bore cleaner -Wipe Out seems to work for me. Plug the breech end with a cleaning patch so that the bore cleaner does not run out of the barrel, and give it a good shot of the cleaner. Maybe keep an old rag wrapped around the barrel a few inches below the muzzle, so that when you spray the cleaner into the muzzle any excess will foam out the muzzle, and you can catch it with the rag. Let the barrel set overnight, then try to clean it.
It does help if you disassemble the action from the stock as this makes it a bit more handy to work with, and decreases the chance of getting the bore cleaner on the stock.
In the morning, try running a brass brush through the bore, then some patches. The brass brush will loosen the crud, and the patches will clean it out. This will work in most cases, but if it is really bad, then other measures may be called for.
If this does not work, then it is possible that the bore has been rusted inside.
You might have to take it to a Gunsmith.