OK, I'm back from the range. Bare with me, I'm typing with one hand, because my right arm doesn't move.
So the recoil is not really the gun's problem. It's simply the matter of physics. The lighter the gun, the quicker the move backward when it fires. For a hunting gun the recoil is not an issue, because that 1-2 shots will not torture you, but the light gun is much better to carry for kilometers. And this gun is really light!
So I sent through it 2 boxes of 3'' Winchester magnum slug, and I have to tell you that it is brutal. The 20 shots of hevi-shot turkey shell weren't much better. After these my shoulder was quite beaten up, but the 250 shots of Winchester target load were OK. With the light target load maybe even my wife (small lady) wouldn't really complain.
But who cares the recoil, here is the problem:
It didn't want to fire the hevi-shot shells. It seems the primer in them is hard, and because of this the left barrel didn't fire them 90% of the cases, the right barrel 70% of the cases. So the first shot from any barrel was almost always a "click".If I cocked the gun and pulled the trigger on the same shells again they always fired. (this means that the shells are OK. The first hit had to "break" the primer cup a little bit, and only the next one was able to ignite them.)
At the beginning (the first 150) the winchester target loads and the slugs were OK, then I started to get a few light strikes on the left barrel. By the end of the trap shooting (220 shots) I had around 8 failures (6 left barrel, 2 right) Only click without boom.

In this situation this model's mechanical trigger has an additional advantage over the inertia trigger: at least the second barrel can fire even if the first one fails.
I added two more pictures about the primers to the end of the album. (click the "full screen" at the bottom left so you can see better
http://yildiz.rscon.ca/ )
My gun is the Yildiz A5 (without ejector)
I think the fit/finish/weight/accuracy is very important if your gun is functioning. If it doesn't, then all those are nothing.
I don't give it up, maybe this problem is caused only by a small dirt/grease in the action or maybe a crappy spring. I'll take it apart if I can figure out how to get to that bolt in the stock and I will continue from there. (if anybody is interested in the end of the story.)