If things are really bad, take the action out of the stock, and warm everything with a hair dryer. Soak a bunch of penetrating oil in there. Put the action in the freezer over night. Thaw it back out the next day, and the brass will have loosened.
And to add to what Leo said, if that does NOT work, then you are into the gunsmith version.
Cast it with cerrosafe, the cerrosafe will grab the brass, then cool, allowing you to remove the whole casting from the chamber WITH the offending particle.
For future reference, I use a oversize bore brush to remove stuck cases. Pull it into the case using a cleaning rod and when you push, dozens of wires grab the inside of the case and out the case goes. Not need for heat, oil, cold. I use a 45 bore brush for a 30 caliber case.