I'm not sure I see how that helps ... you've basically said you'll be running another game with a background of a Zombie infested world. Is that really what you want? (in other words, why do we need the zombies at all, then?)
I think the problem with moving the plot of a Zombie game has more to do with survival; once your characters have enough to survive, you hit the 'then what' problem. Characters have to have a plot hook that motives them to do something other than survive.
Call of Cthulhu faces much the same problems - the characters are confronted with unstoppable or very powerful threats to the existence of reality as we know it. In every Cthulhu game, however, there is a chance to banish the horror back to where it belongs - thereby saving the world, even if nobody knows about it. Since the horrors are out there, they'll keep trying to come back, and you can't tell anyone about it. Good mission hooks and replay-ability.
I think what most Zombie films lack is that sense of mission, and that's why you have trouble moving them into a game - most Zombie films are about survival, and the game 'ends' when the PC's have become strong enough to survive. To move further, you have to have a Cthulhu-esque 'end goal' that will revert the world back to a safe state - which makes replay-ability kind of hard ...
- "Don't assume you are safe because there is a rational explanation for all of this."