[quote=@Synthesis]
Well you have a good concept down to me.
Perhaps a district can only be taken over by completing special actions? (Like convoys, stronghold take downs, VIP assassinations, etc.) Which would probably devolve down into a numbers game of your resources vs the objective require to complete a takeover, or perhaps you can give out special opportunities to increase influence through character interaction. Perhaps different strengths of takeover as well? Where each takeover knocks down the difficulty of control. 
[/quote]

Perhaps something like that. We're just limited on what we can do with written words balance wise.  Otherwise I'd make it like a turn based game where players take turns and then if your people get killed or do the killing it's fair and not just, "Synthesis just made up some tanker truck to throw at me."

EDIT: Also I just noticed in the map that Toxins and Tyre have three bridges and the Chimera have two.  This would mean that the Chimera would be the easiest to defend since they have just two regions to put units at and the other two have three to defend from invasion.