I had a .22 hornet like this once.  I put a lead bullet in the chamber that fit closely, tapped it from the breech with a punch to expand it, and then used a dowel to pound it out.  It took the lead out with it.  I think you're on the right track with kroil or penetrating oil to help.

If that doesn't do it, I'd wrap fine steel wool on a dowel till it fills the chamber tightly.  I'd turn it at slow speed with a variable speed drill.   

Using turpentine as a solvent might help remove the lead; for some reason it gets under the lead and removes it from the barrel wall, and makes it stick to the cleaning patch so it can be removed.  Hard to make this work in a chamber, as there's no way to push a tight patch through to grab the lead.  I don't know if it would help with the steel wool or not.

A third thing that might work is to refill the chamber with cerrosafe.  It might grip the lead and take it out when you pound the cerrosafe casting out.  Then again, it might make the cerrosafe stick.  At least the cerrosafe will melt out again at a reasonably low temp.

As a last resort, heating to melt it out might work, but if it's really lead and not cerrosafe, it will be hot enough to damage the barrel finish before the lead melts.

Good luck!

dave

Put a patch on your cleaning rod, from the muzzle and run it up near the chamber. Then fill the chamber with Xelene or a Xelene/ Toululene combo, such as carbuator choke cleaner and let it soak for a few hours. Then take a oversize, brass bore brush (35 cal) to it and it should push out fairly easily.

Frank