What if phase lanes soaked by friendly culture are impassable to enemies when there is a starbase present? It opens up some interesting possibilities.
Starbases in areas of uncontested culture become tar pits - once you go in, you can't go out without smashing the base.
If you want an escape path in case the assault turns for the worse, push your own culture back at the target gravwell to open up the retreat path. If you happen to have a lot of culture to push, you could simply remove the jump interference. An interesting side effect is that the culture repel rate of capitol ships suddenly becomes critical to hold blockades.
For Vasari and TEC, this means that a Starbase at a neutral gravwell that is 2 or less jumps away from a planet with a broadcast center will protect the jumps behind it. Uncontested with culture, of course. Perhaps Starbases as a whole could receive a minor culture resist, perhaps that of one capitol ship.
Advent starbases can generate their own culture, making their defenses more powerful - but they're already the racial defense specialists, so this fits thematically. It also makes the Deliverence Engine useful for blockade running.
I'm not sure how star to star and wormhole travel should be handled, though.
An interesting play would be when you're pushing a lot of culture at a base but the enemy has several capitol ships stationed, blocking it. You phase in, snipe their caps to let your culture through, and then jump out, skipping the starbase. Makes the support abilities of bases more important.
It's graphically easy to see what your jump options are and probably isn't that difficult to implement. It gives 'area control' to gravwells under your domain without making offensive use of starbases too powerful. I think it might just do the trick.