You need more ram on the GPU. How much does that vid card have? Also more threads equal faster processing time. I have a 15-3570K (4 threads) and I have longer turn times with 35 factions (plus 20 minors) but I am noticing lag while the game 'moves' ships around. I have 16 gigs ram and my card is GTX 970 (4gigs onboard) and it was an amazing increase in perfomance from my previous card which had only 2 gigs on it.
In the end more processors (more threads) is going to be the ultimate winner. I am planning on building a rig just for GCIII using the new Kaby Lake-S 10 and 12 core broadwell processors ( 20+ threads). That combined with faster DDR4 ram 'should' make a substantial dent in turn times and ship movement lag.
GCIII is designed for multiprocessors. Each Ai will use or uses its own thread. I have not heard if this is capped yet so the newer Broadwells (which are behind the Skylakes) in theory would make the game run much faster.
Many forum posts back in beta said GCIII will make excellent use of upcoming multi core processing.
Hope this helps!