Are you 100% sure that the nut isn't sitting too low and that they aren't catching on the 1st fret?

Also, is the string post bar sitting low enough that the strings are pulled down onto the rear edge of the nut? You should be able to take all the clamp bits off the nut and the guitar should play like a normal guitar without them. Get that bar set up correctly and the clamps have a much easier time of just holding the strings in place.