First check your end shake. Press the cylinder all the way to the rear and see how thick of feeler gauge will slide between cylinder face and barrel extension. If it is say .006 pressed back and .001 pressed forward you ave .005 endshake and 2 .002 shims will give you .005 clearance and a proper .001 endshake.
IF you have no end shake and .001 clearance the next think to check is your headspace or rear gauge. With new cases check how much space is between them and the recoil shield at the firing pin. If it is more than .010 you could adjust it by carefully removing metal from the face of the ratchet until it is, then add cylinder shims because this will cause endshake. The max headspace between a .060 rim and the recoil shield is .014 or between rear face of cylinder and top portion of the recoil shield of .074. There are a lot of revolvers out there with max or more head space BTW
If the head space is fine the correct fix is to shorten the barrel extension about. .003-.004.
You can do this fine tooth double cut file. First take the file to a grinder and remove the serrations on both sides so only the flats cut. Then place a piece of duct tap on the back strap above the barrel extension. With cylinder removed, place the gun's barrel in a padded vice so the frame open is above the vice. Lay the file flat on the face of barrel extension and keep it flat as you stoke in the files cut direction. Lift file move and move it back. Place and stroke it flat again. Complete 10 strokes in this manner. Install cylinder and check the gap again. I doubt it will have increased more than .001. It is slow going. Keep at it until you have .004 with cylinder pressed forward. I have done this and it takes time and patience.
The only secret is keeping the file dead flat with even pressure on it. If you are worried about going out of square start your feeler gauge from both sides.
I have the tool that slides down the barrel and both bushings and cutters that do this. Mostly I use that to check myself for square because it leaves fine chatter marks and I get a smoother face with a file.
Anyone who believes this cannot be done properly with a file is uneducated on the proper use of files and what can be done with them. I will bet good money that the old skilled craftsmen that hand fit S&W revolvers often used files to put the finishing touches on the barrel face.
Your plan for taking down the cylinder would work. But first you would need to remove the barrel bushing. You would also need a heavy piece of glass or a granite stone to place your sandpaper on. Once again the trick would be to hold the cylinder dead flat while you stroked it across the paper. It would actually take a lot of strokes even on 220 paper to remove .004.
