I have the same 19-3 as you, down to the estimated year of production. In my case the Hammer Nose installed in this unfired sock drawer special was short and it had a tiny bit of freckling on one side. Note I am quite certain it was 100% unfired because when I took it to the range it wouldn't fire one single round in either double action or single action. So much for the quality for S&W in the late 60's and early 70's. Ordered a new Hammer nose kit from Powers Customs and properly fitted the new hammer nose for a projection just a touch more than the thickness of a dime.
Next time I was at the range with it was a very good shooting day for me. So when I was down to my last 12 rounds I ran the target back to the 50 Yard marker and decided to see how many rounds I could put on paper at that distance. BTW, technically it was an indoor rifle range but it's a great spot for handgun practice because all the knuckleheads use the 25 yard range. I was rather surprised by the results, I had 11 hits on the 14 x14 inch target. I also had 8 out of 12 in the 9 inch outer circle and 6 out of 12 in the 7 inch circle. That's not too bad for free standing and shooting in Single Action.
Point is that you don't have to consider these short barreled guns as short range only firearms. One big plus for short barrels is there is a lot less barrel whip and as a result can be mechanically more accurate than a longer barrel. The only limiting factor is the shooters ability to maintain an "ideal" sight picture and have a good trigger stroke.