Not sure what kind of scripting would be required to make monsters home in on the human player and move towards his town, so I think the first of your two ideas would be the easiest to implement.
That should just be a starting point, though, to get the ball rolling.
The idea reminds me of the Warcraft 3 campaign in which the undead had poisoned the human's grain and the villagers were turning into zombies. On one level, I think, you had to stop a caravan from delivering grain. A mechanic like that could be interesting--zombie faction sends caravans to cities and, if the caravan arrives, the city becomes infected.
If you do this, you could break it up into a bunch of mini-mods, introducing new unit types and structures.
I wonder if you can set structures to spawn monsters. A graveyard that spawns zombies would be cool.
Also, I wonder if you can set monsters to be friendly towards a given faction. Zombies that won't attack other (human controlled) zombies would also be cool.
Maybe you could even make it so human players that get conquered by zombies can continue playing--as zombies! Make it a whole new game mode--last surviving human player wins.
Zombies should have only one movement point.
For changing humans into zombies, you'd probably remove the original unit and spawn a zombie in its place (or replace it with a zombie--if players can continue to play after being defeated). I wonder, though, if you could change the appearance and stats of the original unit. Maybe zombification could work like an enchantment, to change the stats. Since you can change equipment, you should be able to change heads (which seem to work like helmets) and replace normal clothes with tattered zombie clothes; but that would require zombie versions of tons of art assets. Maybe it's possible to apply decals? Or you could just create several zombie clothing sets and associate each with multiple original items. I also wonder if it's possible to change a unit's animation, triggered by an in-game event. Just changing the original unit's animation to zombie-style movements would go a long way. Changing the unit's skin and hair colors, also, which hopefully is possible--and easy.
You'd have a lot of work to do on the economy, too. Farms don't do zombies much good. Maybe zombies can't train units at all, but have to convert them by killing living units--that way you give them a disadvantage and save yourself work.
Human players should all be Kingdoms. It doesn't make sense to have evil, death-spreading, human players versus zombies; and it saves you some work in the art department. Zombies would spread blight like Empires, and they'd essentially be an Empire faction. (This is another point where a mini-mod could branch off. An Undead faction could appeal to a lot of people.)