If you find reaming necessary
OP snagged a real nice K22 with that Model 17-3. As I have found with most all of my 1970's era S & W 22's (3 - Model 34-1 Kit Guns, 2 Model 17-3) they ALL had to be reamed to make them a pleasure to shoot. Before reaming I too tried "polishing" to absolutely no avail. The ladies in my family just didn't want to shoot them at all because of the force needed to extract spent rounds, and the thumb force needed to even chamber fresh rounds!
The Manson reamer, some old Tap-Magic, a vise with plastic jaw liners, and a tin foil small baking pan saved the day.
Curious thing though is that I never had to ream my 1931 Outdoorsman, any of my 1947, 1948 K22's, even an early 1952 never needed anything...the chambers accepted fired cases for dry fire practice and new rounds of any brand, but not so with the early to mid 1970's K22