I have to ask, when you say "cock-feather, hitting the rest," are you shooting a cock-feather down??? If so, that could be part of the problem.

If not, then yes, the rest may not be getting down quick enough, and you need to lengthen the cord. If you rotated your nocks, and you're getting good clearance however, I'd leave it where it is. The longer that arrow rides that rest, the better off you are unless you get contact, then it has ridden too long. But if you can get that arrow to ride the rest until the milli-second it comes off the string, then you have perfection, which is how and why they were designed in the first place.