I’m thinking maybe the zombie attack routine needs to change. All their attacks are bites, but shouldn’t they be grabbing you and then biting you? If you engage and get hit by a zombie, it should be harder to disengage since by all rights, if the zombie got close enough to bite you, they’re probably grabbing you first.
If you’ve played DnD 3.5, creatures could have improved grab, which activated when the creature made a successful hit with a natural weapon. Maybe give zombies a scratch attack that they use. If the scratch attack succeeds, they make a grapple attempt. If they maintain their grasp, they can attempt bites, which are more dangerous than scratches. Getting overrun should be a possibility. Maybe there should be a malus on your further resistance to grapple attempts based on the number enemies nearby or the number of grapples you’ve resisted since the beginning of the turn.
If you’ve played State of Decay on PC or XBOX, there were these huge fat zombies, that would simply grab your head and just bite the hell right out of your neck. Body shots were useless on the things, only headshots were effective.