Hi Tomasz,
I built a simple model of your system in Ventsim using a fixed power for the fans and estimating dimensions of your airways:
I got the same result as you, that is the air is being forced out of the small diameter pipes due to the higher pressure in the manifold. Using one way valves on these pipes would not solve this problem as the pressure inside the manifold would still be greater than that outside, resulting in no flow through the small diameter pipes. The solution would be to go back to the original design without the 37kW fan or use a lower power fan if this is not possible.
Regarding the regulation of the pressure from the screw conveyor, having the regulator in the parallel airway will have an indirect effect on the pressure from the screw conveyor, however this could still be exceeded if other airways were blocked. A better solution might be to install the regulator directly on the screw conveyor.
Hope this helps
Jason