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.