I have a few ideas; some could help solve late game pains.
Keeping with planet classifications from 1 to 10 you can say people can only manage planets of class 9 and 10, that way when you grow your empire to 100 planets you only have 20 planets to manage. The other 8 planet classes that you cannot manage are purely to grow your income, population and research points, that way you will be able to grow a wide and tall empire with little micromanagement, even in late game. That would also make smaller planets a lot more valuable.
It would be nice to see a bit more with Citizens, possibly there could be some special Citizens linked to ideology. Benevolent, Pragmatic and Malevolent traits could unlock citizens that could provide a boost to your empire. Giving the ability to buy some types of ships, possibly colony, constructor or transport ships with ideology points would help to remove the case where you end up with a huge stockpile of ideology points in late game as you have unlocked all traits in your chosen ideology tree. There could also be more ideology specific buildings, some of the Galactic Achievement buildings could be linked to the ideology tree.
Instead of creating trade ships how about allowing the AI handle creating the trade ships after researching trade. Could have other research options to increase the number of trade routes, create convoys to increase the value of the trade routes, research patrol ships to protect your trade routes. Could even introduce trade stations
Could have a fleet manager screen listing all of your fleets and their stats, this would make building fleets and upgrading them a lot easier.
I would suggest limiting influence range from planets and stations as I find that in late game my influence expands and swallows the whole galaxy.
Adding the ability to buy and sell ships on the black market would also be nice.
Randomised tech-trees could potentially cause some technologies to become unavailable negatively impacting the AI. Cross dependency links to technologies and restricting certain engines, weapons and modules types to certain Hull sizes could be an idea. Could also have race specific tech-trees.
I know a lot of people talk about tactical combat, but given how ship designer works it could be difficult to merge the two. It could even come down to having to choose between ship designer and 3D combat, however I have a fantastic idea that could work. How about a turn based, chess style combat system in 3D, with a set amount of moves per battle. It could be in a grid format, weapons can fire so many squares away, ships can move only so many squares in 1 turn, with options like fire then move, or move then fire, retreat from battle, you can have objects in space that effect movement, firing and all kinds of stuff. That way we could have metaverse tournaments, people could design there owns ships, customise the weapon loadouts and fight it out in a one vs one, or fleet vs fleet or whatever you decide. With an auto-resolve option as I’m sure many people might want to just skip the battle.
This is all I could think of at the moment, I’m happy to throw more ideas at you, if you like.