I have set up the 04: Liberty, Mighty MIte, and Justice with the TT and had no problems.

How did you attach the cord on the Liberty? The local archery shop attached it to the loop on the cable slide and it appears that the vanes are making contact.

I have installed most of these rests for bows that we have in stock, so none of the connections were intended to be permanent, just in case the customer did not want the rest when he/she bought the bow. I did not have a vane contact, but anyway (for temp use) I have installed them on the cable slide with a simple knot (easy to undo) and I have installed them on the cables with a string nock. I installed one more permanent setup on a liberty by serving the cord in the cable.

Just try something different.

P.S. are you running odd feather up with your rest. Kind of a dumb question, but I have found that to work better for clearance.

Yes the odd feather is up. With the odd feather up the right feather seems to be making contact with the cord by the knot on the rest itself. I guess that because the cord is attached to the cable slide it sits in an "up" posistion instead of a "down" posistion if it was connected on the cable. This is all a learning process for me.

I've got both my bows set up with it served in the down cable, works great, no contact at all. I think TT says 1 or 2 inches below the rest.