Ow, my head hurts. But yes, if only visiting/returning from the west, you neither enter the WZ, nor do you need a wag bag.
As for the original hike being planned, IMO the n->s route is preferable. Going down Carillon, up MR and down Discovery is better than the reverse.
Also, taking your time going up Shepherd helps acclimatize for the rest of the trip. It's also one of the more scenic trails - the canyon is immense.
