You can try the springs then, but be sure to rigorously test ignition of whatever the carry ammo is. Check Numrich's for the triggers. Also, Call S&W. They have a ton of stuff not on their web site. What 36 do you have that has a serrated trigger? My memory is fuzzy, but most I've seen have smooth combat triggers; I've had two 60s and two 36s over the years and I think all (vintage 1968 to 1986) had smooth triggers.
Another comment is, if you do go to a gunsmith, make it CLEAR to him that he is not to stone or file on the sear notches and faces on the hammer and trigger. The reason is that the hardening on those parts is about .003" thick. As soon as you make a few strokes, it's gone, and you are down to softer steel. It will feel great for a few hundred or thousand rounds, then starting wearing to an unsafe condition. I have seen this so many times it's nauseating. The customer leaves with a gun that feels slick as a snake. Then later on it starts stepping off the sear and, Yikes. Unless they are a professional shop prepared to re-harden or re-chrome the parts, this is bad.
Given what you have added, I'd say get a Wolf mainspring and possibly a rebound spring. When you have the gun down (detail stripped), polish highly the faces of the rebound slide itself and also the recesses it rides in.
When you reassemble it, use first just the mainspring, leaving the rebound spring stock. Now try it a while and see what you think and if it's reliable. If it's still too heavy, then consider going back in and changing the rebound slide spring. Far too often, changing both at once makes for unreliable ignition.
For help with this if you don't know how to do it all, see Sylvan_Forge's excellent Model 10 thread stickied at the top of the revolver sub-forum. Great stuff. The J is slightly different, but not much.
PS - I did not mean to sound like I was talking down to you before. I now see the "firearms instructor" in the by-line, which I overlooked before. I just saw the fewer posts and made an assumption. If you are good at breaking down guns and moderately mechanical, you can do this stuff yourself with the right caution and instructions. That's also why I added the littany about why you might indeed want to do it yourself or at least communicate well with the gunsmith about not altering the sear and notches.