Quick lesson in double action shooting.
Shortening the pull requires serious alteration of the geometry of the trigger and hammer. Rather expensive and ABSOLUTELY not required.
First: Get a decent pair of grips as VictorLouis suggests. Either the rubber Pachmayer type or (my preference) Herrett's Shooting Stars. Make sure they fit your hand. Grip fingers should wrap around far enough to get a good hold on things. Trigger finger should engage trigger at first joint.
Second: Dry fire. Use both hands, cycle trigger through while watching sights on a plain blank wall. Concentrate on tip of front sight. Goal is to drop hammer without bobbing the sights. One single continuous pull; like ringing a doorbell. Not jabbing, not taking forever, just "in - out". Bing - Bong.
Third: If you feel you must have some action work done, have these steps executed.
*Fit cylinder star to hand. (If the 'smith doesn't understand what you want, smile sweetly and go elsewhere. Do NOT leave gun.)
This is the process wherein the lobes on the extractor star are matched to the hand that rotates the cylinder. This is the adjustment that smoothes out the pull. There are several (one for each chamber) lobes on the star and one hand, so the star much be fitted to the hand, not the hand to the star.
*Fit internal trigger stop.
*Install quality aftermarket springs.
*In some extreme cases, the primary double action hump on the trigger must be reshaped.
"Polishing the action" can be done. It is expensive and merely replicates what you do in dry firing.
Age... I bought my 581 revolver in 1981 or so. When they first came out. It's still ticking. My 44 Special was purchased second hand, but dang near unused in 1974. I've a couple of K frames purchased as "police trade ins" with no concept of age. But they shoot really well.
I see you live in Chino Hills. I'm in Long Beach. There are possibilities here.