Some trivial, perhaps misguided musings:
Start in the direction opposite the nearest zombie. Continue until you are equidistant from $N > 1$ zombies, then go along a direction bisecting the line segment between any pair of them. You have two (nondegenerate) choices: towards or away from the pair. If the pair are sufficiently close to each other, this strategy requires that you go away from the pair.
In this way this strategy can lead to a trap in certain conditions for $N > 2$, but typically $N = 2$. So let's consider this case. The pair effectively merge once they reach the bisector. At (or before) that point you have a new pair, typically with a different bisector (amusing aside: the atypical case is akin to a "pickle" in baseball: http://en.wikipedia.org/wiki/Rundown). Again, you may have two choices, or only one.
It seems to me that the key in a proof would be to show when this strategy (which I think is plausibly optimal in at least some cases) allows you to increase the distance to the nearest zombie.