Looks like there are as many ways to clean revolver chambers
as there are shooters.

I chuck the gun (with rubber stocks installed) into the rifle
rest with the cylinder unleashed. Holding the cylinder in my
left hand I run a long 45 cal. bronze brush, with a patch of
solvent (Butch's Bore Shine) over the top, chucked into a bat-drill
into each cylinder. A few seconds of action and you are done.
I change the patch every other cylinder. Then I degrease the
chambers with brake cleaner on a patch with a jag.
I don't do much to the cylinder face. Just wipe it off.

I never shoot specials in a magnum chamber. That's what
the Special guns are for

...Nemo...