On Morwen's suggestion to scale rewards: That has the unfortunate consequence that losing is a favourable outcome. It would be still doable by making LP prices (sink) decrease with diminishing territory but by making LP rewards (faucet) decrease more rapidly. This could be accomplished by for example making the rewards bonuses/maluses linear to amount of territory control (from 0/nSystems to nSystems/nSystems = 1) and the prices some kind of an S-curve.
The result of this would be that having a high degree of territorial control, while good for farming LP, would not be an ideal position to cash the LP out. Similarly, while LP gain would be lower while losing, when the S-curve dives sharper around the midpoint means that any LP gained thus far can be used to buy more toys. For the metagamers, this would mean that a back-and-forth wave motion is preferable to status quo.
Additionally it is notable that both functions (for LP payouts and for costs) cannot be on a linear scale, but instead both halves of the parameter ("number of systems occupied") need to be normalized on the initial amount of systems. (For example, Amarr have fewer "originally Amarr" systems than the Minmatar do. This would mean that in order to reach the equilibrium point between payouts and costs, Amarr would need to hold at least a few Minmatar systems, whereas psychologically, the equilibrium could be thought to be the situation when neither side controls any systems originally belonging to the other.