Sounds like a strange one...
The Model 19P was a fixed sight piece made for export to Peru. These were made in the late 80's, I'm guessing 87 from what's printed versus the s/n on my 4" version (AWFxxxx). There were 4"ers and 2.5"ers, most that I've seen were 4", only looked at one 2.5" piece, and it was VERY nice.
The M19P was too late to be recessed, as that practive went away in 81/82.
The piece you describe could be a one-off factory piece or ??
Your comment "It had a 3" barrel with the ejector rod shroud (not like the 3" M66 but more like the old M27) " is a little confusing, as the M66 and the M27 both have barrels with shrouded ejector rods, so cannot tell what you are saying.
Do you remember if the extractor star was blue or nickel?? Factory nickel guns all had blued stars, this is one way to determine if the piece was legit or re-nickeled outside the factory.
It could very well be a factory 3" gun that was gussied up for a special order, but I've never heard of one nor heard anyone talking about any fixed sight M19's other than the M19P. Never say never with S&W, there are certainly a lot of variations out there. For confirmation on this, the best and only way to check is call Roy Jinks, the S&W Historian at 800/331-0852, ext. 223.
Good luck.
.......SmithNut