Yep, the feathers are the reason for the good flight with contact. That's a rest that has the control cable attached to the cable slide so you're stuck with it that way unless you change rests. If you can't rotate the nocks to get the fletchings to clear, and you can't adjust the cable guard out a touch, a different rest with a control cable hooked into the down cable of the bow may be the only option.

Edit: You might try moving the prong assembly out on the rest control bar one set of screw holes and then sliding the whole control bar and knob to the right to get back to center shot, that should move the control cable to the right as well just enough to get clearance.