Contact can happen with any setup, but I'm guessing that your arrows are underspined. Ya might be better off with something in a 300 spine. For a quick check just take a turn or two off the limbs and see if they fly any better, especially with the broadheads on. Then you'll know if spine is the issue.

Not totally sure about the cams on your bow. Cam lean (idler) can also cause a right tear through paper. And for your info there is no reason to shoot through paper at 20 yards. Normally the fletching has the arrow almost straightened out by ten yards. If it doesn't then you got some really big issues.

OK, for tuning you could try walk-back tuning. This is for setting centershot. It will have nothing to do with nocking point location. It really sounds like your rest is too far left. That's another reason your arrows are flying to the left the farther away from the bow you get. Walk-back tune it.