I feel your pain & as for pulling the hammer slightly & spinning the cylinder, I've watched Jerry Miculek do this many times, right or wrong. Just saying. He does it in the opening seconds of this video.
Jerry is doing it to be sure theres no resistance in the cylinder function, Ive done it many times, slower than jerry does, the difference is why and how, as in not letting the cylinder locking bolt slam up into the bolt notch while its spinning. The primary offender besides dirty 22s, is 45 acp rounds, the chambers on many have a burr or ridge that hinders complete seating of rounds, though on some guns shooting cast it can get gummy and sticky to fully seat or eject after enough rounds are fired. This varies in different guns. In a ruger 45 with acp cylinder I had, it would do it clean with lead bullet acp reloads, all of which functioned perfectly in auto pistols. After a cylinder or two, it became more of an issue, and a few more rounds fired, can bind to the point that the gun isnt going to keep shooting. Forcing the cylinder around a couple times manually, NOT forcing it by cocking the hammer or trigger action in a DA, but turning the cylinder by hand, pushes the shells down enough to work, but it gets progressively harder to do.
A friend had this problem in an S&W ACP revolver, one of the stainless guns probably from the 90s, others in various makes and models. Some remedy this with throat reamers, which is good, though expensive to buy a reamer. Alternately, Ed Harris described using a 30-06 case drilled and tapped for a bolt in the back to spin it in a drill and using lapping compound to lap out the ridge at the front of the acp chamber. I tried it with the Lee case trimmer pilot holder with the drill nub on the bottom for a Uberti acp cylinder. It worked. It was somewhat surprising how sharp and distinct the ridge or burr at the chamber was when first putting the case in the chamber and spinning it. It cut a pretty significant groove in the case. The friend successfully fixed his S&W by the drill and tap method and a 270 case.
22s seem to vary considerably in how many rounds they can run before needing cleaning. The family k-22 will generally go around 1000 rds or so before it starts getting gummy to seat and eject. I used to shoot a lot of the old winchester wildcat rounds, cheapest available at the time (1980s), plain lead bullet, heavily waxed, and shot fairly well. Other people say they can get a few cylinders full before they start getting gummy, or a few hundred rounds. Its enough of a problem that theres a chamber reamer loaner on one of the forums to fix it. Im not sure I buy the idea that the chambers have to be crazy tight to shoot well. the family gun shoots well despite a fairly substantial number of rds through it, and no particular care in choosing loads.