I have a little experience with this. My tier 4A New Holland T9.615 developed an intermittent miss or I would call hiccup when warmed up. It would puff a little smoke that you could see in your shadow but you usually couldnt even hear it. This unit did have a def puck on it. My dealer could not find the problem and told me it is possible I have a plugged up exhaust. They would not go any further until I looked at or removed the inners of the exhaust. Well I opened it up and it was a clean as a whistle. This is after 4 years with a puck installed. For those not familiar with the inside, it has 3 different layers of what I would call a honey comb ceramic material with small openings. Picture each layer about the thickness of the air filters in these tractors. It is not easy to get to the top one. I couldnt believe how clean it was, cause like you say black smoke can be seen at times. But it was bright white with no trace of soot on any of the 3 layers.
So, what turned into over 2 years of chasing this miss, ended up being a wiring harness that had rubbed through. I found out this harness was a very common problem on the red and blue four wheel drives from a different dealerships service manager. I knew it was common when my dealer had the harness in stock and this is for blue which is a different part # than a red one.