I suspect that your arrows are underspined profusely. It's pretty well established that when you approach 70# with anything around 28" or more then you should be shooting a .300 spine. It's even possible in your shorter arrows. There is a way to find out.
I would try backing down the weight to see if this is indeed the issue. At least two turns, which at about 68-69#should still give enough oomph for anything walking this earth.
I wouldn't get too excited about the arrows grouping at longer ranges. YOu can get almost any arrow to group, even if it's way underspined or over spined, with field tips.They might fly ugly but they'll group.It's when you put broadheads on that things can really get screwy.
I think I would download Easton's Tuning Guide (
www.eastonarchery.com) and tune for broadheads. See if this helps.
You're seeing something else. Paper tuning isn't all it's cracked up to be all the time. It tells you what the arrow is doing as it leaves the bow, but not what's going on down range. And I've never shot a deer at 6'.