Though its always a good idea to replace the stock Stoeger firing pins with stainless ones....longer lasting and more reliable.....I don't believe that is causing your problem. Or, that there is a problem with the springs.
Have experienced the same problem(usually with left barrel, though), myself. It's likely the locking bolt isn't going forward far enough, to securely lock the barrels into place....so the action is open slightly. 'Off the face' is the term usually used for this condition. Why?
To achieve a certain price point, Stoeger guns aren't fitted with the same care as more expensive guns. This is especially true with action fitment, ie: locking bolts and lugs. Take a look at the wear mark on the top of the front locking lug. How much of the top surface of the lug does it cover? If less than half, or not evenly worn across the lug's top surface; then the locking lug isn't coming as far forward as it needs, to secure the barrels onto the action face and fully engage the hammer springs. Plus, the surface of the lug is not flat and square to the locking bolt. At the factory, the locking lugs on these guns are likely just given a couple of licks with a file, until the action closes. So quite often, locking bolt/locking lug fitment is less than optimal. That is the likely source of your problem.
Does it happen more often when the gun is closed slowly, or with low to moderate force?
What happens here is that, as the locking bolt moves slowly forward, not enough spring pressure is available to drive it forward with sufficient force, So, it jams into the uneven surface of the lug and bounces back slightly, rather than sliding evenly across the lug and locking all the way forward. So, the gun's action pops open a hair, enough to cause it to go out of battery. Try closing the action with a good snap. Did the gun fire more reliably, this time? This time, spring energy was released faster... driving the bolt forward more energetically. So the gun went into battery. But this doesn't completely solve the problem.
Luckily, the cure is simple. Any competent gunsmith can fix the problem,in a matter of minutes. Or if you are handy with tools and careful, you can do it yourself.
One good resource for working on Stoeger(and other guns), is the 'Marauder' web page. This site is filled with useful information on how to tune these guns for optimal performance. Worth a look.