This is how I would do it:
I would borrow some ideas from Star Wars: Rebellion. I would combine the concept of both "leaders" and "activation tokens" so that leaders are what you activate your systems with. I would possibly also combine the concepts of the Strategy cards, Political cards and Action cards into a single card type and use them in a similar way to how missions are in Rebellion: you either activate a system with one of your leaders to move ships there, or you activate a system to attempt a mission (one of these cards) in that system, with each leader having specialisations in different areas (military, trade, politics, etc). Opposing players can send their leaders to try to oppose your missions.
I would try to find some way to make combat faster and allow more players to participate during it. Maybe players in adjacent systems can "support" one side or the other in some way...?
I would also offload all special abilities from the different units and move these on to technologies instead. Having to explain all the different unit abilities to new players is probably the biggest roadblock of getting this to the table with new groups.
I also agree about streamlining how tech works, with no classic "tech tree". I would also make the tech names easier to parse so it's more obvious what they do without having to read all of the text! Maybe even combine techs with the "missions" idea above and just make them another type of mission you have to complete. Also agree with somehow removing the planet cards. Maybe also combined with my idea for mission cards above, at the end of each round each planet lets you draw a certain type of mission card, or something like that...?