It just so happens that I was working on a map for EOFS for me to GM. Here's the skeletal version of what it looks like:
The concept behind this map is that it's structured around a trade spine running from Byzantium to Leagueheim. The jump routes along this route are long, letting you quickly traverse the galaxy while other jump routes are shorter. The five homeworld locations are indicated, which homeworld starts in which location is something I figure the players would select. The Symbiots are in the upper left corner, blocked off by Stigmatia.
My intention with the blank worlds on this map was to first randomize them but then dabble with the settlements so that worlds near the spine would be richer then worlds near the periphery. The flip side of this would be that the rebel units on the worlds close to the spine would be strong while the outer worlds would have fewer rebels. On the other hand there would be the worlds near the symbiots, which wouldn't have any industry but would have symbiots on them (apparently the last garrison commander was incompetent.) There would be more bonus resources on these worlds to compensate for the lack of settlements and enemies. The richest worlds would be the trade spine worlds themselves. These would have industrial chains already set up but would be heavily guarded by rebels. These worlds are supposed to be a valuable prize due to their wealth and location so that seizing them is just asking for conflict with your fellow players. So the different parts of the galaxies all have different advantages and players should chose their starting positions based on the strategy they wish to pursue.
As a house rule with this map I would ask that Terra and Leageheim be off limits for player invasions. Neither the Church nor the League would have scepters. These worlds are just supposed to be where the trading ships set out from. The Vau are absent. Each noble house has a scepter on Byzantium as well as four on their home world. There are additionally will be five scepters placed on random worlds throughout the galaxy.
Each of the ministries would be given a "homeworld". The Garrison would have an industrial complex on the first spine world, the fleet on the second and the imperial eye a complex on the world in the upper right that only connects to Byzantium. These would create house resources that players would be allowed to sell. However there would be an imperial audit carried out by the GM every once in a while that would publish how many units a player built for the ministry. Players would be free to create political fodder from how diligent someone is in building up their ministry. The precise details of how many ministry resources are built and sold would not be published, just the ministry units built and lost. The eye would not get audited in this fashion.
The starting units of the ministries would be scaled back. The Eye starts exclusively with spies and invasion landers, no heavy infantry. The Fleet would be smaller and be more focused on destroyers with fewer cruisers/dreadnaughts. The garrison gets no fleet at all but does get battle stations at Stigmatia. The ministries are less about the starting units and more about the free industry.
Finally I would want to do this with an accelerated start. I'd devise a point system (based on output value of settlements and input cost/tech of units) that would allow players to purchase additional settlements and locations on their home world and on worlds adjoining their home worlds. Players would send me their requests in secret and I would edit the starting map accordingly.