Jeff, isn't your barrel already installed in the rifle? I think your making this more difficult than it is...
Remove the barrel from the frame. Should be just one screw/bolt holding the forearm on the barrel, remove the forearm and the barrel will separate from the frame by using the lever to open the gun.
Use a flat head screw driver to remove the firing pin housing, clean the firing pin/spring (don't loose the spring it will have some tension) add a drop of oil, reinstall like it came out and your good till next time its needed.
I only clean the firing pin area after a range session or at the end of hunting season, depending on how many times the gun was shot.