A couple of points:
First, the serial number (3077) on the sight you found is almost certainly not the complete serial number----more likely the last digits. This practice was (very) common on pre-war target guns.
Next, The treatise on S&W target sights has already been put together----for quite a while. Specif. "The Evolution of Smith & Wesson Target Sights" by Robert J. Neal was published (in two parts----front and rear) in the November and December issues of Arms Gazette------1977. (!!!) And it is "comprehensive", covering all (but one rather obscure) rear sights and virtually all the front sights.
Registered Magnums were fitted with what we have come to call the "Two Screw" rear sight-----as were later .22 Outdoorsmans, 38/44 Outdoorsmans, M&P Targets, the K-32 1st---and perhaps some more I've overlooked. The "two screw" rear sight has THREE screws---one at the front to attach it to the frame and the two at the rear-----one to adjust elevation and the other to lock that adjustment in place.
And while all (I think) Registered Magnums carried the horizontal scoring below the rear blade, the same treatment appears to have been available on order for other guns. Translation: I have seen such treatment on other guns. I don't know if it was done by the factory or not.
Ralph Tremaine
And the 2.75" LOA sight you found is for an N frame-----the K frame sights being 2.5" LOA-------the I frame sights being 2.25" LOA-----and I know neither the frame size designation nor the LOA for a Ladysmith Target's rear sight----nor do I care. (!!!)
And I just remembered a couple of more guns with the "two screw" sights-----the later .44 HE 2nd's----and 3rd's.