I used to have a Stag M4gery. Good little gun if you're into that kind of thing. Mine wasn't any louder than any other 5.56mm rifle. Does yours have a muzzle brake or a flash suppressor? I suspect you may be stuck with the former, since you're in an Iron Curtain state.
Are you shooting inside? All centerfire rifles are super loud inside. Maybe find an outdoor range if this is the case.
Isn't Stag in New Britain? You might give them a ring and see if they can change out the barrel or muzzle device.