What about triangles?
What occurs to me is that world maps are always rectangular images - why not make a geosphere, then use the triangles on that as locations - each location is a single polygon, can be numbered depending on the polygon number. I think it could look quite cool, especially considering you'd have a round planet, with markers on it, rotating around. I think it would be novel to be able to loop around the planet, unlike the normal layout - you could start from any location and spread out from that, expanding your area rather than a cut-down version of risk.
A geosphere provides the most realistic shape - whereas a DBPro sphere works in rows and columns, a geosphere is made from equi-sized triangles. It's a similar grid to hexagons, however I personally think hexagon grids look dated. I would make a standard sphere map and normal map for the planet, then make maps for each battle location - then zoom in on the planet and load up the terrain and stuff for the battle. This would allow you to set however many polygons, or locations are on a planet, maybe even have moons with capturable zones. Having a good old fashioned planet take over scenario would be cool I think, and a real planet is a good way to represent the big picture.
If you want to give it a go, and need some geosphere models, I'd be happy to make some for you, not all modelling packages can do it.