a little different is almost a given, 12"'s is way way too much. You definetly have an issue that needs attention. You could site it in to hit where your pins pointing but I think you'd have some real issues in between pin shots.
I'd first off pic one arrow and shoot it, start dialing heads and points in. Get them closer, moving the rest for starters making them no more than 2"'s different then walk back tune with the broadhead. Stand close and hit dead center high enough on the target that as you walk back the impact can travel down the target, but not to high as you'll probably shoot over the target before it drops until things get dialed in. As you shoot farther and father away from the target always using the same pin the arrow should drop plumb down from the dead on shot (Make them good until your sure you did). If they drop straight down, that's good. If they make major drops, 6"'s or more at every 10 yards back, that's not so good, your arrow is coming off pointing down and the BH shows it. I believe you have the exact opposite going on now. If they drop down at an angel they are coming off sideways and a left or right adjustment needs done.
There are other reasons but, I'd bet that is it. FOC, too much FOC can make the head dive, to little can make it float causing the nock to drop, I don't think that's your case because most arrows sold today all come ready to shoot, not saying they can't be improved, just saying they can be shot with most heads sold without to much trouble.
For fun stand about 20 yards away and shot at the center of the target the step up to 7 yards and shoot with the same pin. Make sure you have something behind the target, I'm thinking it's going right over the target. I set my bow up to make both those shots with the same pin, just a tad low at 20 yards, but low is better in my book.
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