RE: weird paper tune
Well, if you want better results you can paper tune farther away. That' s the problem with paper tuning. If you keep backing up, the paper tears will " lie" to you. Paper tuning is designed to catch a " snapshot" of the arrow as it' s leaving the bow. The farther away you get, the more your fletchings will correct the flight of the arrow, so your paper tears will not represent anything of use.
Mahly13 is correct in that you get different tears at different distances. You can be " way off" but set your paper up at a distance that catches the arrow at minimum flex. Lied to again.
If you' re shooting carbons or thick aluminums (17 wall, etc.), I' d recommend bare shaft testing. That is, shooting a regular arrow and one with the vanes cut off (leave the base and glue for weight, just trim off the fin) at the same target and compare their impact points. The bare shaft planing test is not done through paper. You just shoot at the target, and see how far away the bare shafts hit from your fletched ones. Unlike paper tuning, the farther you back up and adjust, the more precise you can tune. Start at 10 yards and back up once you get them impacting close together. This test tells you how much in-flight correction your fletchings are having to do.
As far as your rest centershot, remember that torquing the bow can effect where it should be set. The farther the rest is left/right of where your hand hits the throat of the grip, the more sensitive it will be to torque. If you are torquing the bow, you can get two tuning points. How? Picture the bow from above. Lets say you naturally torque the bow clockwise " two hours" on the clock face. Well you could set your rest up to the left of center (at a distance equal to 10 o' clock) and when you draw the bow you naturally torque the rest into the 12 o' clock position (straight ahead.) You could also set the rest up to the right of center (distance equal to 4 o' clock) and when you draw/torque, the rest moves into the 6 o' clock position (once again straight ahead.)