Since the Fleet Starbase and Embassy are temporal instances, you cannot use them as a true "fleet house" like people uses the Earth Space Dock or other permanent instances. Fleet Starbase and Embassy should have a permanent instance system that allow em to serve as "Fleet Housing"
Since we're limited to refine 8.000 Dilithium units, it would be nice to make this part of the game more "Free-to-Play", allowing Dilithium buyers only aesthetic advantages, as in other F2P games.
That way, it would incentivate members of the fleet to invest Dilithium on their fleets.
Another possibily is making the Dilithium from the items purchased revert to a "fleet dilithium" storage, that only could be used by those who has permissions, to distribute and contribute it to the current projects (and it would appear in the leaderboard by "Fleet Dilithium Storage" or the name of the fleet)