Just spoke to Benelli/Franchi. TSS is fine with their factory chokes. I ordered an extended modified to try, which is a .600. In their extended chokes, full is a 590, IM Mod is 595, and modified is 600.
I tried the 585 and 593 already, so the 600 should help, I hope. Will post results once I get it. To not confuse anyone else, their flush chokes are different constrictions for F, M, and IC than the "extended" chokes for some reason.