Yep, nothing beats the smooth trigger pull of a S&W revolver that's a K-frame (like your M19) or larger with its leaf mainspring. And an incredible trigger is one of the most important things in how well any firearm can be shot!
Are you having any misfires shooting the revolver single action (thumb-cocking first), or just via shooting it double action?
T.
PS: The strain screw SHOULD back out counter-clockwise, though it will be fairly tight to turn. Possibly you may want to put a couple of drops of penetrating oil on the strain screw's threads and let it sit overnight. AND . . .
Always use hollow-ground screw driver bits of the correct size that can be purchased for guns at gunshops. They won't mess up the slots on your screws like the old mechanic's type screw drivers!
Also, sometimes folks grind off the tip of the strain screws so less tension is put on the leaf spring with the screw is turned all the way in. NOT GOOD! In this case, it only involves ordering a new screw from S&W.
Other folks would grind material off the leaf spring . . . again thinking it would make a "lighter" trigger pull. Look for the dreaded evidence of Mr. Dremel Tool on the face of the spring. Leaf springs are cheap too . . . and it is an easy fix.
If these things don't fix it, a firing pin nose that's too short to contact correctly might be the culprit.
All these things are very, very simple for any gunsmith to inspect for quickly . . . and probably he won't charge you for a quick inspection unless you need parts.
New parts for S&W K-frame revolvers are both cheap and plentiful all over the US!
Hope this helps,
Tom