I suggest the Mollweide projection
It has to be a cylindrical projection so that it folds over cleanly.
Hmm.. This would be rectangular without being swedocentric. It's not perfect but much better, at least for games where the north isn't important...
https://en.m.wikipedia.org/wiki/File:Equirectangular_projection_SW.jpg
I like that one a lot. It's like a compromise between the horrible Mercator and Gall. And with that you wouldn't have as much distortion of travel distance east/west vs north/south.