What specs do I need to run the largest maps?

I have never actually done it, but I've heard GC3 can actually chew through more ram than that at the highest setting.  Since your PC is probably eating 4+ just idling, odds are you're hitting the point where you start paging the drive.

You should run the game with some system monitoring tools up though, see what it's doing.  It's possible the AI is chewing up your CPU before you start paging and just doubling up your ram wont help, I've never had any interest in running a game that big myself.  Vishera's aren't actually 8 full cores, it's much more like a hyper-threaded quad core.  Depending on what kinds of resources the game is using, you can have quad core performance as they bottleneck on their shared resources.  They're less shared than hyper-threading on the Intel side, but still susceptible to zero gain scenarios and I don't know nearly enough to say if GC3 is one of them.

I  run Insane all the time.  Memory is your biggest helper. I run a 4 core 3570K and had 8 gigs. I was stuttering and lagging on insane mid game. I since upgraded to 16 gigs and a better video card (gtx970). NO crashes, no issues. Late game with 40+ factions i have longer turn times but that is because i only have 4 cores. If i had an I7 then I would have 8 cores and my turn times 'should' be faster than what I have now. 

I plan on getting the 8 core I7 and DDR4 next year with the tax refund. I build it around GCIII actually. I also will get a 4K monitor but I am still waiting for Display port 1.3 to show up.