You aint getting sub MOA out of 55FMJ cause the standard rule of "garbarge in, garbage out" applies to rifles too. Sorry, but if you want to play the subMOA game, you gotta shoot subMOA ammo. If you dont reload, you might want to look at starting. Its a fun way to make great ammo at reduced costs.
The privi stuff is OK, but its still not going to do what you expect it to do. You know the rule, you cant polish a turd. Shoot turds, expect turd groups.
As for the 223/5.56 thing, about any commercial ammo you buy is going to work fine in that rifle, functionally, but if you want to shoot subMOA, which most of us do, you are gonna have to break bad and cough up some $$ for the right commerical ammo, or save some serious coin and roll your own. You can get some Nosler 2nds, run them on a Dillon 650 at a rate of about 600 an hour, using cheap ball powder and once fired brass and it will shoot as good or better than the Fed Ballistic stuff.
Again, not trying to be harsh or a smarty marty, but you will find that most of us on here, at least those of us that shoot competively, arent going to "know" much about factory ammo as we shoot too much to afford to buy factory and we expect more out of ammo and tailor it to our rifles.
Get some Black Hills remanufactured with some 52 or 53 grs SMKs and try those if you have to stick with factory stuff. Your 12 twist is going to limit you to bullet weight too...dont have a slow twister, but I am thinking that your talking nothing even as high as a 69gr SMK in that, but one of the other guys will know for sure on that one.
John