Most, if not all the TDA (DA/SA) semis only specify the minimum SA trigger weight. You want to make sure you don't go below that on a carry gun. I personally "had issues" with shot placement during our service pistol trials with guns that had a major difference between DA and SA trigger weights. That's probably something that much practice could cure, I decided I didn't want to bother with the issue. Apparently, many of the other testers felt likewise.
OP in your situation, I'd have the action smoothed and leave the springs alone-so long as the SA is still within specs-and see what the results are. Do try to find out what the SA factory spec is for your gun. Most of the S&W TDAs had 4.5 lb minimums. I personally found something a wee bit heavier worked better for me, around 5.5 IIRC.