As of Beta .91, influence is pretty much a dead mechanic. As you say, culture-flipping doesn't really work and I don't have any ideas of what would fix it. I think it would be more than getting Brad to tweak a few magic numbers. In Civ VI, culture-flipping has a purpose – to prevent wanton forward-settling and to encourage an alternate play style for certain leaders. However, in Civ you have dozens of settling options. In GalCiv you only have a few so buffing the culture-flipping mechanic would make the game even more dependent on your starting position.

IDEA: Increase the radius of the telescope takeover so that you don't have to manually scout basically your entire sector. Maybe that would help reduce the "oh crap, I sent Theia right towards AI territory and now I'll never find any good planets before the AI grabs them all." If you did that, it might be easier to consolidate an empire and make influence stronger.

Influence is better done through Communications Starbases (for culture flipping). But you are right that Influence Districts are just generally weak. I'm going to boost their adjacency bonus, giving +2 to other Influence improvements and +1 to adjacent approval districts.

I love my communication starbases, but I do pick my targets carefully. I set some up along the Drengin border when the Dengin were the top player in the game. They did not like it and did exactly as you said. Declared war and took out the starbases quickly.

Fortunately, I love the Manti because of all their Survey Command ships and had gone heavy into them. I recalled all the Command ships before the Drengin started going after my planets and with some support from regular ships we had a command ship fleet vs command ship fleet that wiped the Drengin fleet out and left me a few survivors.

The big drop in the military might affected both of us. But I had tried to talk the YOR into declaring war with the Drengin (YOR were #2, I was #3) and they were unwilling to. Until, that big drop of military might for the Drengin. Suddenly the opportunistic YOR were open to the idea and I gave them a lot of techs to make it happen.

The YOR desended on the Drengin like an overcharged roomba on a bowl of spagetti. A few turns later the Drengin were begging me for peace, which I accepted so I could rebuild.

Then I began to realize my mistake. Between the techs from me and laying claim to the Drengin empire on this overloaded map the YOR will become the real threat I have no good way to deal with. And left out of the drama has allowed the Mimot to do their Mimot thing and I now have massive Mimot fleets flying around just looking for a ripe target.

Rather than try to beat the YOR to the Drengin resources that they are all over I decided to turn to the Navigators. They had a few good colonies that were swept up by my post-Drengin war fleets and I know have a transport ship laying siege to their homeworld. As long as the plan holds steady I'll have a good infrastructure of worlds in place by the time the YOR finishes off the Drengin.

But, the YOR won't have much influence on their newly taken worlds and the Drengin are going to hate the YOR for as long as the war lasts. It would honestly be a good time for me to replant my communications starbases and see if I can flip some of these worlds to me while YOR are occupied.

Another nice buff to influence could be the ability to trade starbases in not matching control zones. We had it like all starbases could be traded and now no starbases can be traded. Maybe this concept could be a nice tradeoff and a motivator for influence.