my thought was that the game could use (and these titles are just off the top of my head so feel free to comment) "approaching fog" and "waning fog"
Approaching fog: game starts with no fog of war. as the 2nd round starts, a fog starts to settle in disallowing you to see regions that are 5 moves away (5 is an arbitrary example and can easily be replaced with a diff #). on the 3rd round, you can no longer see 4 moves away from your occupied regions (again, number is arbitrary but it will always be the round 2 # minus one). the 4th round, the fog moves one closer, and so on until a full fog of war.
Waning fog: begins with fog of war. 2nd round leads to you be able to see 2 regions away from yours (as the fog begins to lift) the 3rd round the fog lifts a bit more and so on.
This is a pretty flexible suggestion that can be tweaked but I think it would be really fun. I do not know much about computer programming and such so I do not know if it would be easy to implement but if so, it could prove interesting.