And one more thing? Ditch the 'they won't eat each other' bull. Every other species will, if hungry enough, eat their own, and these things are never NOT hungry.
If you do that, their menace diminishes because then all you have to do is outlive their hunger. They will eventually eat each other.
One of the defining pre-requisites for the zombie genre, in my opinion, is that the world has spiraled fully out of control and there will never be anywhere truly safe again.
Obviously World War Z
takes liberties with that idea, but you get the picture.