I think that a designated river feature would be great for this game. Instead of players having to use normal water tiles to simulate a river, there could be some way to place a separation between two land tiles, preventing a nation on one side from crossing to the other, but you would still be able to place river crossings at certain points like normal.
Basically, rivers would not take up any space, but would simply act as dividers between land tiles, this way if there are two cities sitting across from each other, one on each side of a river, they can be placed right next to each other, but the river can still play a part.