That's an unusual mix of features. Serial numbers a little below K200000 are mostly from the last few months of 1953, long before the top sideplate screw was designed out. The first four-screw K-38 should have a serial number somewhere around K300000 and should probably have shipped in 1956. I don't know how to square the seeming disparity here.
Can you post photos? I don't doubt you, but I like to gaze at things that challenge common knowledge.
Ah, that's good solution! At K286xxx you are probably pretty close to the beginning of the four-screw K-38 Masterpiece serial numbers. That gun perhaps shipped as early as late 1956, but because S&W had no policy of shipping in serial number order, it might have sat in inventory for a few months before leaving the factory sometime in 1957.
Beautiful gun, by the way. And that box looks unopened! (Insert envy face here.)