Thats really really odd. I've got an FX 8320 and I've been playing around with performance tonight, haha, no intent on playing these massive games with current micro hell, but to each his own.
I just loaded 54 races on insane, and I have no problem with the first turn. The game does AI work during your turn (non-interactive calculations), therefore as soon as the game was ready, I launched soak. It took maybe 40s on the first turn, and subsequent turns are about 20s each. For whatever reasons (actually, Windows scheduling issues), GC3 is using only 6 of my 8 cores. If I read forums, or multitask during the soak, cores 7/8 are used, and the game doesnt slow down. As well, during my first turn, none of my cores have gone over 50%. This pisses me off, but I suppose this is due to optimization GC3 has done for Intel and not AMD, plus AMD is indeed less efficient per core than an Intel, even though AMD general has fast clocking speeds (wont go into that debate rathole).
The FX 9370, I just read the specs and some reviews. Wow, its supposed to be NUCLEAR
However, everyone warned of temp issues. Do you have water cooling? Are you sure your cpu is operating at max frequency? The 8320 is rated for 3.25GHz, but I've got it overclocked and stable at 3.92GHz. Windows task manager is falsely stating I am at 3.5GHz however. Several other 3rd party cpu monitors all tell me 3.92GHz as well, so I have faith my OC is working fine. When playing world of tanks, I could never OC my memory (actually, it would only work when lower freq than rated compatibility with motherboard), however on non-multicore games like WOT, a single core was always maxed at 99%. perhaps the memory OC didnt work well at high cpu-util. anways, I have my memory running at 1800MHz now. I'm running win8.1. apparently Win8 has a lot of multithread improvements over Win7.
If performance tweaking isnt the issue, then I just think there is some AMD/Windows defect causing this. I'm not sure how much mult-threading takes place during that initial turn 1 setup phase. Best bet would be to find someone playing GC3 with a 9370 and compare.
Good luck