I did a basic game a while ago where there was no character creation at all, and any time you died you just got a new body and kept going. It was a heck of a lot of fun and the players absolutely loved it.
So, consider this: in zombie movies, there's ALWAYS more zombies. Each time you die, roll a 1d10 or something to pick your zombie type (much like Left4Dead, really) and that's it, you're good to go. Now try to eat some heads! Give the zombies a goal that they can accomplish through brute force (such as "eat or kill the soldiers holed up in that building, so you can then eat the civilians inside"), and any time the players try to plan too much have their head explode due to too much attempted thinking. And then go nuts. Don't bog it down with die rolling any more than you have to... a very simple system like "for every action that needs to be randomized, roll 5 dice. Any 5s or above are successes. The difficulty of the action determines the number of successes you need" and then adjust the difficulty based on what sort of zombie they are. Thus, a pouncing zombie only needs a success or two to jump on someone's head, while a shambling zombie would require five successes to do it (but only 2 successes to survive a gunshot without being injured).
JaronK