I haven't been playing this game for that long, but it doesn't take a seasoned player to realize how overpowered mobile Star bases are, even in AI games.
My vote goes to making all Star bases stationary, that will effectively put a stronger emphasis on positioning and strategy respectively.
Diversity is great between factions, but there are a billion other ways to mix and balance faction specific mechanics, i don't see this being such an issue to remedy.
Speed is really the main factor for balance. Developers having control over that speed is necessary. If a starbase can still move slow enough to intercept a constructing starbase in a gravity well yet have difficulty catching an enemy fleet all by itself, I would consider this balanced(yes, vasari don't have building destroyers, their starbases are both tougher and they have minelayers and overseers which are both the best units of their type, and will ensure that you can build up a powerful starbase of your own in that gravity well, which will move faster then other starbases allowing the vasari starbase to build up its attack/defense capabilities).
The point is if you build a starbase in your gravity well, as the defender, you should have a larger advantage.
Instead of a dynamic where "one races moves, the others don't", you can have a better implimentation that allows you more control over game balance by "one race moves decently fast, the other is slower, the most powerful is the slowest".
It COULD be powerful in certain situations, yet so COULD most of the endgame abilities available. Fleets have more ways of getting wiped out in one hit, and in my opinion, this is a good thing. It truly gives players more ways to measure each other and themselves by. If something COULD be OP in some situations, yet not all, then it actually COULD be balanced. The frequency of the tactical situation needs to be taken into effect as well, some abilities are inherently overpowered because the tactical situation is likely to occur multiple times in every game, where others are super strong abilities where the tactical situation might never appear in a game.
If your opponent dances around your inherent strengths as a faction, then this is attributed to either luck or skill, depending upon the ability. Either way, its not overpowered as its avoidable.
How avoidable something in factors into how OP it is as well.
A moving starbase is very avoidable, as you don't have to really face them on the defensive. Sure, you will see more "attack starbases" by TEC and Advent, yet at the same time this strategy won't be nearly as easy to achievebecause of the surprise element is greatly diminished due to the clunky slow nature of the TEC and Advent starbase constructors.
Slow constructors increase the amount of time to get to the area, which increases the risk associated with scouting.
Also, in single player play, If a moving starbase makes things easier for you, then you can do something.
You can increase the difficulty level of the AI you face(which makes you feel more like a "badass singleplayer").
If facing max lvl AI, face max lvl AI and another AI opponent in a 2v1 scenario.
The game's scalability is its strength, learn it and love it singleplayers!