Screen for syrups with pulp and fruit pieces

We just recently started making syrups with pulp and fruit in it, but our screen is a 10 mesh and it is filling too slow and clogging up.  Does anyone know what juice companies do for a screen?  According to FDA your screen needs to keep things from 0.3 inches from passing through.  According to that you only have to have a 3, 4, or 5 mesh screen.  Does anyone know of where I can special order gaskets with screens?  Online I can't find anything smaller than a 10 mesh.  The diameter I need is an inch and a half and two inch screens with gasket.

Like a tri-clamp screen?   https://www.sspseals...i-clamp-gaskets  (Maybe)

I think you are kidding yourself that a 4 mesh screen will efficiently remove long slender pieces (such as 1mm x 8mm).  That's almost a 5mm opening.   

I made juice.   We did not screen juice for FM control.