As a big zombie fan (I even have a book about zombie behavior) I have some suggestions.
I have not read through all 30 pages of chatter, so maybe someone else already suggested some of it, but what the hell... :)
*) Zombies are stupid. Therefore, if there is no activity in a territory, they should not understand that there is "food" there in that territory, hence no attacks would occur. With activity means deploys, attacks, movements, reinforcements etc. - called "noice" below.
*) Zombies are attracted by noise. Therefore, since they go last, where the round have had the most kills would be where they would be interested to attack/move towards. The more noise the more number of attracted zombies moving from territories not directly adjacent.
An illustrating example: If in one turn 3 territories has been attacked, where respectively 10, 20 and 30 troops has died (combined losses from both sides), the zombie army would (if unlimited) move 3, 6 and 9 armies (if possible) towards those territories from territories (in each case) randomly within 2, 3 and 4 steps away
*) Zombies have a keen smell. If too many zombies start to flock in an area (5 or more), and there is a non active target next to it that hasn't moved for 3 turns, eventually a zombie will get a sniff and they will attack.
*) Zombies are dead troops. Therefore the number of zombies per turn could be based on the number of armies killed each turn (divided with 3 for example), although I think it is better to just keep it capped at that the zombie army get territory troops (1 per 3 territories).
*) Zombies are dead troops. They could therefore be deployed closest to where attacks have occurred, divided on number of dead troops if there are several attacks that has occurred.
An illustrating example: If in one turn 3 territories has been attacked, where respectively 3, 6 and 9 troops has died (combined losses from both sides), and the zombie army has 6 armies to deploy, they would deploy 1, 2 and 3 armies to the territories that they had closest.
*) Zombies are slooooooow. They are dead remember? Therefore, they should only be able to "walk" 1 step at a time (reinforcements).
*) They are zombies. Therefore, they don't stop attacking because they are down to 3. They keep going until they can't move any longer. They should at the most stop attacking at 2. (Then they get easier to kill too.)
*) If they succeed with an attack there should be a 50% chance that they keep attacking adjacent territories. This also mean that they will randomly attack (until dead or succeeded) 1 out of 2 adjacent territories, and 1 or 2 out of 3 adjacent territories, and 2 out of 4 adjacent territories and so on.
/ Paul K