Stoeger Uplanders have issues with their firing pin set up, especially the left side. It can be fixed by a good gunsmith. I havent attempted to fix the problem on mine yet, been to pre-occupied with my reloading set up.
Soft primer strikes are a normal thing for the left side because it uses the longer trigger mechanism. I was testing what mine would eat and it didnt like Remington 00 buck in the left side but it was ok in the right. Winchester 00 buck would feed in both sides. You're not the only one having the problem, so dont stress out. You may just have to switch to a different brand of shells until you can get the problem fixed like I'm having to do.
By the way, which model do you have? It sounds like you have one with exposed hammers.