One thing that may make this easier for you guys is something I noticed recently…… The status of bordering territories is frozen when a mission is taking place there. They will not gain any zombies. So, I recently experimented with starting missions constantly and canceling them halfway through. You’ll need one person for every bordering territory, but it seems to kinda work in holding things to a reasonable level.
Quick note, though. The zombies will increase the same no matter how many bordering territories you have open. It’s just that the max zombies on one square will get reached a lot faster for where you aren’t doing missions. An easy way to see this occurring is to to conquer all zones except for one in the corner of the city. Then wipe out all the zombies and wait one turn.
The zombies will be back.