If you really want polar movement, how about this...
A cuboid world!
Each face of the cube would be a square of say, 100x100 tiles (for total tile count, that would correspond to a 256 tile world map in current versions of civ). Six such squares would make the entire world. The only issue would be that on the corner tiles, diagonal movement in certain directions would be impossible. Also, if you are on the 'north' or 'south' face of the cube, there is the issue of which way to orient the screen and consequent keyboard mapping.