Howdy
Good photos.
The 4th change can be difficult to pin down because they were produced from 1915 until 1942, and Serial Numbers ran from 241,704 to 1,000,000 with 758,296 produced.
As AZAndy stated, the factory did not keep records of when they were made, only when they shipped. A factory letter from the S&W historian will tell you when it shipped, and probably where it was shipped.
You can ask for a letter by following this link. The cost, at least the last time I lettered a Smith, is $50.
https://www.smith-wesson.com/firearm-history-request
The number under the yoke (crane) is an assembly number. It does not mean anything.
Your SN on the butt is the SN of the gun. It should appear in four places: Bottom of the Butt, underside of the barrel, rear of the cylinder, and underside of the extractor star. This last spot is often difficult to see. If the number is the same in all four places, it means the gun shipped with those parts.
That style of grips (Walnut, Square Butt, Round Top without Medallions, was typically put on S&W K frame revolvers about 1920 to 1929.
The shape of the knob at the end of the ejector rod looks a little bit later than the 19 teens to me. Generally, the smiths from that era had a mushroom shaped cap at the end of the ejector rod, like the one on this 38 M&P from 1920.
The cap on yours is just a little bit larger in diameter than the rod, so there needed to be less of a clearance cut for it under the barrel. Later, S&W did away with the separate cap, the end of the ejector rod itself was knurled. Less parts, and less modifying of the barrel.
The other interesting thing about your 4th Change is the marking on the rear of the hammer.
REG.U.S.PAT.OFF.
It stands for Registered U.S. Patent Office.
This was an attempt by S&W to keep cheap foreign imitations out of the US market. S&W trademarked the case hardened finish on their hammers and triggers, and stamped them so. If you look at the rear of your trigger you should see the same marking. By trademarking their revolvers this way, S&W was able to keep cheap imitations out of the US for a while. Eventually the courts threw it out, and S&W stopped marking them that way. I don't have the data in front of me, but I think they were trademarking their hammers this way in the late 1920s and the 1930s.
Anyway, the closest I can come with my Smiths to your SN is a 4th Change with a SN of 6212XX which shipped in February of 1934.
Yours probably shipped a little bit earlier.
P.S. As carefully as you can, remove the grips. Don't pry them off, undo the screw, and if they don't drop off gently push one off by gently tapping on the screw on the opposite side. See if the grips have been pencil lettered on the underside with your SN. I forget which grip they lettered, so look at the underside of both grips. I'll bet those are the original grips. Look carefully, the pencil probably has faded over the years.
For what it's worth, I never replace nice old grips like that with modern ones. I like to keep my old Smiths as original as possible.