For SS only...
First, I remove my S&W's SS cylinder (One screw holds the yoke/cylinder - use the proper hollow-ground driver!). Time and different solvents may help. I alternate between Hoppes and Breakfree - work them in with a nylon brush - allow more time to soak - as you should for the barrel & cylinder bores. Clean the frame opening, etc, while you are waiting. The last cleaning should be with a stiff nylon or brass ((Not SS!) brush, then wipe away with a paper towel. The 'shadow' left will have no thickness and present no problems operationally.
Of course, I'm anal... a drop of Flitz or dab of Semichrome paste metal polish in the fold of a cotton swipe will do to return the original SS look to that cylinder exit face (Probably give that CS blued face a bare metal look - for a while - too!). In fact, a small swipe will actually do for 2-3 revolvers - it doesn't take much if you allow a solvent to do the majority of the work. The discoloration is much 'softer' than the SS cylinder face - so I am not worried about metal loss there. My range denizens/comerades marvel at my 'clean' revolvers. I generally clean cf revolvers every trip, too. I often think that folks like blued revolvers because they both don't show nastines as readily and you have to be so careful cleaning them, many just don't!
Some time back, I wanted to see just how filthified my 625JM could get and still function. I often bragged how it - and an ammo box of 'clipped homebrew ball ammo - was my Zombie protection. I got to over 800 rounds in a couple of months - only wiping the frame/barrel/muzzle a few times with a rag. It still worked fine... I just was too embarrassed to be seen with it so nasty - and cleaned it. Maybe I am being anal cleaning so much.
Stainz
Just because there's a stain outside the cylinder, that doesn't mean your gun isn't clean. The stains are natural byproducts of blasting ammo at high velocities, pressures, and temperatures. Once in a while I remove them, but mostly I like the "lived in" look.
