There is a lot of confusion about when model numbers start showing up. Too many people assume they were shipping in 1957. The decision to use them was made in the summer of 1957. However, it was not implemented instantaneously. Very few, if any, model marked guns left the factory in 1957. For the most part, they didn't show up on dealer shelves until 1958. I personally have never seen a model marked S&W revolver with a
confirmed ship date earlier than 1958.
Some examples:
The first Model 29 shipped in January, 1958. Some non-model-marked .44 Magnum revolvers may have actually shipped later.
.22/32 Kit Guns with no model marking shipped as late as June, 1958.
A K-22 Masterpiece with serial number K311xxx is not marked as a Model 17. It lives in my safe.
Management decided about changes, but it was up to the floor supervisor to determine when the change went into effect. He had to deal with production, and production decisions involved things like using up parts (including frames) on hand, scheduling various models for assembly in an order that matched up with sales demand and other factors. Keep in mind that all models were not in production all the time. They were made up in batches, so some models would run out of old parts sooner than others.
A four screw i believe, five if you count the one under the grip.
Your .22 Combat Masterpiece would be a four screw. The screw on the front strap of the grip frame is the mainspring tension screw and does not count. The four will consist of three in the sideplate and one in the front of the trigger guard.