It's not just the Z71 and max tow packages. I have the RST non-Z71 and like previous pick-ups it too fishtails on washboard roads. Unfortunately this is the worst I've ever seen and I buy a new chevy every three to four years.
Like others have said, adding weight to the back will help but it's not going to go away completely. Bilstien 5100 shocks also help but there is no real solution. Heavy springs designed for the payload/ towing wars combined with a now lighter weight back end means more fishtailing.