OK, here's another tip (not that you don't have enough already!).
BE SURE GUN IS UNLOADED!! Take a small stainless steel bristle brush (available at Home Depot in the paint section), soak it in Hoppe's and brush the solvent into the face of the cylinder and let it sit overnight. Use it liberally! Let it sit overnight. Get up in the morning and, after your second cup of coffee, hit it again and - voila! - the scorching will come right off! I do this to my SS guns once a month when I fire 'em and it works like a champ and NEVER leaves any scratches or brush marks. Be sure to hit the forcing cone and underside of the top strap in the same manner. While you're at it, check the front of the cylinder crane and frame where it seats in the battery position. Lots of crud will build up there as well.
If you really want to do a bang-up job (no pun intended), using a well-fitting gunsmith screwdriver, remove the front screw from the sideplate being VERY careful NOT to damage the screw slot and GENTLY slide the cylinder/crane assembly off the front of the frame, indexing it with the frame as you go. When you have the cylinder & crane assembly in your hand, just slide the cylinder and extractor rod assembly off the crane (to the rear) and you'll have the entire front face of the cylinder to work on without having the frame & crane in your way. Press the extractor rod to the rear and clean out the crud under the extractor star and where it seats on the rear face of the cylinder while you're at it.
Reassembly is the reverse of disassembly. Good luck and be sure to lubricate all moving parts of the cylinder & crane with a light lubricating oil before you reassemble the gun!