My suggestions would be for the various races to have different types of drives, reflecting how they move across the board. Outreach had a pretty much straightforward drive whose success was dependent on the ranges involved.
I'd suggest a drive that uses warp points that could lead anywhere in the galaxy once established, leading to a "scattershot" empire with holdings anywhere on the map, but linked by the warp points once established. If you wanted to make it really hard for em, make it a one way trip, or totally randomize their destination with each jump. Then you'd have the classic Starforce drive, limited in range but fairly dependable. A Starfleet / Star Wars drive would be capable of various speeds across the map as their drives improved in range covered per time used for the trip. 1 hex, multi hexes, anywhere on the map. Or a Stargate style transport, where you could be anywhere on the map once the transfer gate was set up for a given location. The other major aspects to be considered on a generational scale game would be the races attitudes towards others and internal politics, as well as the envirionment conditions/hazards on the map. Just a few things to consider in developing the game. Keep it simple, but offer options is probably the best way to go. Outreach always was a favorite of mine, even in solitare mode due to that. If you need another playtester, add me to the list.
