OK ImpalaCustom, I'm going to trust you here since you have seen the inner workings of the single set triggers and All I can find is Winchester's original blueprints (Wisners) on how to make the parts.
I think the trigger assembly might be missing a pin. On rifles without the set trigger, the part Winchester calls the knockoff which is just above the trigger has three pins. One pin is the pivot pin. Right in front of it is a smaller pin which works against the flat spring for spring pressure/trigger return. The third pin is in the lower part of the knockoff and engages the trigger in the slots on both sides of the trigger. So when the trigger is pulled it rotates the knock off up into the hammer sear in the top of the reciever. The one I am working on does not have this third pin that engages the trigger.
So, my question is - Do your set triggers have this third pin that interacts with the trigger???