The problem really doesnt sound like it is associated with the set trigger but perhaps another problem within the lock?
Usually, if the set is too light you cannot get the hammer to stay in the full cock position.
To adjust that set trigger, make sure the screw in between the two triggers is backed out say 1/2" and then place the hammer in the half cock position. You then advance or tighten that screw until you hear the lock snap. When that happens, back the screw out one full turn. (Please note that the hammer will stay in the half cock position while you are doing this)...You can repeatedly Set the rear trigger then snap the front with your finger to check the operation with that hammer again, being in the half cock position.