Easiest way to remedy this is by making zombies have to be registered players only. Registering is already easy to do. But that comes with a cost of new players having a harder time to navigate or tryout what the server offers, so my second suggestion is by having two zombies game mode, one for the registered players and one free for all.
I often see that it’s always unregistered players cheating, and by having a separate game mode for registered players makes it easier to ban them if they were cheating due to having unique username.