Every replace a pilot bushing in the end of a crankshaft?
I haven't tried it but it might work -
get a dowel rod close to the same OD as the ID of the barrel.
See if you can use a grease gun to pump some grease into the barrel. ]
When the barrel won't take more grease, use the dowel rod to push the grease into the barrel.
Once you've got grease coming out of the barrel around the dowel rod, or you can't push easily with just your hand, take another piece of wood, or a wooden mallet, and smack the end of the dowel rod. Keep adding grease and smacking the dowel rod till you've got the air out of the barrel and it only has grease and the dowel rod in it.
It's using hydraulic pressure. Its amazing how easily you can remove a pilot bushing out of the crankshaft.
I've even used soap (carve off slices with a knife and push into the bushing). Not sure if it would work in this case, but it might work better than grease since the "viscosity" of soap is higher than grease and it wouldn't pass between the barrel and dowel rod as easily as grease.
As I said, I've never done this with a stuck round in the chamber, just with pilot bushings in gas engine crankshafts.