The main problem with that ideal is that there is no sense in puttiing resources into culture, as any military victory would remove any culture victroy. If I put resources into culture and win a culture victroy, it would be use less under you ideal, as one military victory would lead to a military and culture victory. All I'm saying is that the culture, should give more of and edge to your side if you put more resoures into it, instead of the military side. This means that if you lose a military victory, you could still when the next time thougth your culture power.
I would like it, if I win one victory and the AI the other, that we both are still in the fight. But your ideal Williamnight is that if I win one vitory, I win it all. But I understand your side of the plan. If I win the space battle, I should also win the culture battle, but this comes in the from of destroying boardcasting centers and from my captial ships.
An ideal I was working on, was to give the board casting centers abilitie to control a form of culture warfare, in which you could select a culture program that changes how the cultures react when they meet each other. The plans could be set in a rock, paper, scissors in which one could counter another. This means that it is easyer for players who use there culture programs will to move there culture into an enemy system(in order to increase the military power when they attack that system).
The plans are all based on ground forces, which include power armors, taht are ships into the enemy system, to anything elese that fits the lore of that faction