Bare shafts consistently hitting the the right of your fletched arrows and a left tear through paper would seem to indicate the same thing is going on when you release an arrow, just that your fletching is correcting what the bare shaft can't. It doesn't sound like you are too far off, but I would try to get them to hit together.

Do the bare shafts seem to be flying straight to the target?

Two things you could check without throwing your rest off would be changing point weight, or changing the draw weight by turning the limb bolts. Of course, if you are bottomed out, you can only turn them one way.

The other thing might be to try to be careful with your grip. I have had a few bows (with reflexed risers) that I could shoot bare shafts well, but only when I was extremely careful not to torque the bow or the string with the release. Your grip might be causing what you are noticing.

Personally, I don't like to bare shaft tune aluminum arrows. If they are not hitting the target straight point on, they can bend. Then your bare shaft tuning exercise becomes impossible, unless you have a straightener. I guess even with carbon, you should spin them frequently to check their straightness, although what can you do about it if they wobble?