Same question here. The fact that the game can't multithread, in terms of the CPU or GPU, would explain why our great systems can't play with too much more than 150 men on field, but the fact that others with lesser systems are doing it makes me wonder if there's something I can try. Have you tried all the known tweaks? If you do and something works, let me know...i'll do the same for you. I've tried many tweaks, but no go.
BTW, if you haven't tried tweaking your graphics card (gpu) in the Nvidia control panel, I'd start there first.
1) try setting the pre-rendered frames to zero, and see if there's a difference
2) you might want to try different drivers, esp. older ones--make sure they are right for your 560ti
3) I too have an EVGA, and I use the EVGA precision app to monitor my gpu usage, and temperatures. You can even use it to overclock your gpu a little and see if that helps at all. Just do NOT overclock and also check the Windows Start Up box selection...if the new speeds you select crash your pc, when it reboots your GPU will be at it's default speeds again and not starting up with the system crashing overclock specs.
*that being said, it's likely your cpu is causing the limit and not your GPU. Your CPU is just fine, but the game it seems is more CPU processing intensive than GPU, but ya never know if a gpu setting is limiting things until you rule it out. When I set my battles to 400-600 men (low fps and stutter occur), my gpu is barely used which tells me the hold up may very well be my CPU. Even overclocking my cpu doesn't seem to make much difference--I just don't think the game engine is really coded properly to be able to handle too much more than 150 men. However, others with less system "claim" to be able to, so what gives?