Howdy
Us 44DA owners have to stick together.
Mine is chambered for 44 Russian and I have no problems with pierced primers.
First off, see if you can get a measurement on how far your firing pin is protruding through the recoil shield. It looks to me as if it may be protruding a bit too far. Here is a photo of mine, it protrudes right about .050 when the hammer is all the way down. I had to pull the cylinder off to get enough clearance to get the depth gauge part of my caliper in there, but then it was easy. Notice that my firing pin is also down near the bottom of the hole. I do not think position is a problem. Extra protrusion is more likely a problem.
Here are three fired cartridges from my DA 44, still with their fired primers in them. The two on the left were fired normally. The one on the right I put back in the gun and dropped the hammer on it a couple of more times. Notice the dent is significantly deeper. The hammer on a gun like this stops against the frame. But I also noticed that when I chambered the brass with spent primers the hammer did not bottom quite all the way. It was about .020 or so from all the way down. You can do the same test, with once fired primers. You will have to lift the latch to see the position of the hammer. If you lift the latch, and then slowly open the gun, you can see if there is any movement of the hammer as the spent case is moved away from it. What this means, at least in the case of my DA44 is that when the firing pin strikes the primer, the hammer has not fallen quite all the way, by about .020, but it is enough to fire the primer and the firing pin does not pierce the primer.
Lastly, here is what my firing pin looks like. Notice the little 'nipple' at the end. I do not know if that is how it left the factory, but it works quite well. You can actually see in the protrusion photo that just the 'nipple' is protruding through the hole, and it is relatively blunt. This gun has been refinished at some point, so I do not know if the firing pin shape is as it was when it left the factory. But I get no pierced primers.
I notice the end of your cylinder rod looks to be threaded. If so, that is not the way it left the factory. The extractor star on these guns was a separate part brazed onto the cylinder pin. It was not too difficult to break one off. I suspect at some point somebody threaded yours in order to refasten the ejector star, which may have broken off. Be sure the end of the rod is polished smooth or it will tear up the depression it fits into in the recoil shield.
My advice about the pierced primers is to first find out how far your firing pin protrudes through the recoil shield before you do anything.
P.S just noticed the bit in your first post about the jury rigged cylinder pin.
P.P.S. Dunno what the story is with your recoil shield. You can see it is not the same as mine. Does the SN on the cylinder match that on the butt of the gun? Perhaps that cylinder was substituted to the gun later. The cylinder should have the SN stamped on the rear face. You can just barely see it in one of my photos.