Thanks for the "I enjoy cleaning guns and tools" comments. My family doesn't understand why I spend an hour in the garage after a range session. My Dad, as well, taught me to keep tools cleaned and oiled. Every time He used even a screwdriver, he used an always available mineral oiled rag to simply wipe the blade before putting it on his well-organized tool wall.
Are you using a hollow ground screwdriver? I was worried about using a regular screwdriver to remove the cylinder, so I bought the S&W screwdriver set on Brownells.
Personally, I've never heard of anyone getting sick from cleaning firearms. I suppose it's possible, but I usually scrub up pretty good when I'm finished. When I reload .45 Colt, I use cast lead bullets, and I wear gloves then, but I'm also directly touching lead for several hours, rather than particles for 15 minutes 4 times a year. Thanks for watching!
I tried your method and it didn't work for me as well as it did for you. The method I use is a scotch-bright pad attached to a Dremel Mandrel. The scotch-bright pad literally scours all the dirt and carbon fouling off of the cylinder. After doing that I tried your method and polished the cylinder to a mirror finish. I love my stainless steel guns but I hate shooting them because I know I have to remove the burn rings from the cylinder.
Along with take care of your tools & they will take care of you is a Place for everything and everything in it's place. Always return things back where you got them from. Two things I passed down to my three sons. Funny I do the same thing to my 686+ because the burn rings take away from the beauty of the gun.
Quick fix, if the ejector rod comes loose don't force anything just stick either a tooth pick or a wedge of wood under the front serrations of the ejector rod and pull the hammer back just a little bit and then hand rotate the cylinder counter clockwise and it will tighten it enough to work so you can swing the Cylinder out.