Hello!
First things first, having played since the original Galactic Civilizations released, with thousands of hours logged on both games, let me say how thrilled I am the third game has been announced! Absolutely thrilling! Definitely going to get the Elite founder's kickstarter! 
But I digress.
The previous two games used a rectangular play grid on the main star map, with each square having 8 "adjacent" squares that a ship could move to. I propose that in Galactic Civilizations 3 you instead use a hexagonal grid, with squares replaced by hexagons and attached at each face for a total of 6 possible movements.
I understand that this would reduce possible freedom of movement for units, but this is my intention; if GC3 is even remotely like GC2, then late-game turn cycling will take decades due to the AI calculating all possible future moves and doing stuff (See: Civilization 5, Total War Rome 2 etc...). Restricting movement using hexagons reduces the number of calculations the AI has to do by orders of magnitude while still appearing elegant to the eye, while also looking more "futuristic" and "fluid" than the previous grid. Beyond that, it would also make star systems and other cosmic phenomena look more natural and pleasant looking. Combined with the inevitable technical improvements, this could seriously improve game performance.
There you have it; a justification from a technical and aesthetic viewpoint. Do you agree, disagree? Anything in particular you see wrong with this that I, a tech illiterate missed?
Example;
Squares
9 x 9 x 9 x 9 x 9 x 9 x 9 (Move seven spaces) = 4782969 possible movements
Hexagons
6 x 6 x 6 x 6 x 6 x 6 x 6 = 279936 possible movements
This already large discrepancy between the two increases to unbelievable number the more things you move, and the more you move them.