fastetti - I experienced a similar problem with a Martin Bengal a few years ago. It was driving me nuts. And I know my solution is going to probably get me a lot of bunk from some other members but here it is anyway. I had a sneaky suspision that it was the Ripcord arrow rest causing the problem. So I switched to a NAP Apache dropaway rest and the problem went away. And to prove my point, I took the Apache off of my Firecat (which was tuned perfectly) and installed the Ripcord and the problem came back. I believe the older Ripcords (like the one you have) aren't fast enough to get out of the way of the fletching.
Well that was my experience - take it or leave it.
BTW, I don't paper tune anymore. I set up for centershot and then use the walk back method followed by BH tuning.. Works well for me and I have been shooting better in the past 8 or 9 years than I have the other 40+ shooting a bow.