To start with it came without a firing pin, so there was a problem there at one time.
Check the channel the pin fits into for burrs ect that may slow it down. Check the new pin also for any burrs that ride in the channel, stone them if so. I have had one that had a slight bend in it and caused mis fires, after straightening and stoning smooth it works well.
Add two #10 machine washers to the rear of the mainspring to add preload pressure which increased hammer strike.
The third thing would be to modify the pin itself, I know it's new but they come with a step in them the outer one hits the rim and causes the ignition, the inner one stops it from hitting too hard. If yours it just a few thousandths off it will cause a misfire. I will post a picture but make sure you take matierial off the lower side that does not strike the rim allowing it to strike deeper with more force.
Go through the steps to correct the problem one at a time, I can only surmise what is the problem from here, sometimes a simple stoning or the washers do wonders. Hope you do well, I shoot fed bulk in my 39A and 39AS and have no problems now, but had failure to fire or extract in both at one time in the past and have done all I advised you.