Customizable Generation of Home System

Maybe some kind of point-buy-system (where you could buy additional planets and improve their quality (terraforming, resources, size)). 

I think one of the earlier civilization games had something like that. And I really liked it. You could use points to buy population, tile improvements, military units, buildings, ...

Or it could be tied into faction customization. This would probably be a lot easier to implement, but would only influence custom factions (with fixed presets for existing factions).

And for op: As a workaround in the current game you can just start new games until you like your home system. Annoying, but works.