Do you use some kind of muzzle guide when cleaning the barrel to avoid dinging up the crown ?
That's worth doing, or else be
very careful not to let the cleaning rod touch the bore.
When cleaning a revolver, I always remove the cylinder and crane, and let them soak in a jar of Hoppe's No. 9 while I'm cleaning the rest of the gun. If the cylinder chambers and face are unusually dirty, I let the parts soak overnight.
A Lewis lead remover is the best way I've ever found to clean the bore and throat, although sad to say, it's not made in .22 caliber.
Most people don't do it this way, but I'm something of a cleanliness fanatic. Every third or fourth trip to the range, I strip a revolver to the frame, clean everything within an inch of its life, oil liberally, and reassemble the gun. That's a bad idea if you're going to store a gun longer than a few months, since oil tends to coagulate.
A week after I clean and oil a gun, I push some dry patches through the barrel and cylinder chambers. A little extra-last dirt comes out about as often as not. I've never understood why, precisely, but revisiting a cleaned gun takes less than five minutes, and improves one's peace of mind.