I'm glad that the problem has been worked out. I've used a cleaning rod to clean my musket and it hasn't gotten stuck in over 20 years. Not a period cleaning rod but it does the job and doesn't get stuck.
But, something I've found that works if the cone is what is stuck and the threads are exposed at the top of the barrel and this solution is kind of like putting the handle on. Drill a ramrod diameter hole in a piece of shelving thickness board. Put that on the exposed ramrod and then screw a tool or ordinary nut that fits the threads on the end. Then tap the board away from the stuck portion with a hammer. This won't move the rammer much with each tap but you will notice progress until eventually the whole thing comes out. I've tried (and seen others do it) the tug of war and have never seen it succeed. If the tool is stuck, a slot cut in the board would allow it to slip around the rammer to give you something to tap.