The Hunter is complex but usually works fine if unmessed with & clean, properly inletted & hasn't been 'adjusted' by someone trying to improve the system. It's the other half of the mechanism,,the sears,, that must be adjusted correctly. Specificly the sear arms that contact the trigger assembly have to be in the exact correct placement and spaced perfectly above the triggers contact points. Too low to the pads and they may double or make the selector not operable. Too high and you may have an overly long trigger pull or not enough trigger pull length to even get the thing to fire. Plus, too high over the pads and the interupter will prevent the barrel selected from fireing at all. Other things figure into it too,,a long heavy sear nose engagement will make the interupter engage on the selected barrel before the trigger breaks and prevent fireing. The sear arms must also clear the trigger engagement pads after fireing to allow the interupter to disengage and the second barrel to be fired. Lots going on in there thats not necessarily inside the Hunter trigger mechanism itself. The shotguns tang screws should be properly tightened down. The final adjustment to getting the trigger working properly (assuming the trigger mechanism is in itself working correctly!) is in the tweeking of the sears, the placement of their arms, the sear engagement. Getting the trigger to function by backing off on the tang screws is actually telling you what the final corrections should be done.
It should not be the way to just 'make it work'. A loose stock and fit up will result over time and even more problems result if the gun is an actual using shotgun.