Great looking revolver, congratulations. I have a 44 magnum four inch four screw with serial number 176XXX. It was shipped in July of 1958.I recently came into this lovely Model 29 no-dash with a very low serial number of 184021. Sending off for a letter on it now.
The closest 4" units I find are:
S183936 - shipped May 4, 1960
S184076 - shipped May 5, 1959
Doc (Bill Cross) might be along to give you a definitive answer or a very close estimate.
As you can see from the above, they didn't ship in anything resembling serial order.
BTW, here's a 4" Model 29 with an interesting serial number - S184184. It shipped on February 12, 1959 (Lincoln's birthday). It is also interesting because it shipped with smooth rosewood stocks.
.I am adding a few photos of my 29. It only has three screws and it has a left hand thread ejection rod. I may need to get a letter to find out more, but this combination seems rare. That number over the mod-29 matches the serial number on the bottom of the grip frame.I don't have that number in my records, but some very close shipped in late 1958 to early 1959.
Bill