Your experience indicates to me that your cpu is your limiting factor.
I think League is mostly single threaded, and possibly can make use of 2 cores.
To help clarify your CPU/GPU options, run these two tests:
a) Run your games, but lower your resolution and eye candy.
If your FPS increases, it indicates that your cpu is strong enough to drive a better graphics configuration.
If your FPS stays the same, you are likely more cpu limited.
b) Limit your cpu, either by reducing the OC, or, in windows power management, limit the maximum cpu% to something like 70%.
Go to control panel/power options/change plan settings/change advanced power settings/processor power management/maximum processor state/
This will simulate what a lack of cpu power will do.
Conversely what a 30% improvement in core speed might do.
You could also experiment with removing one core. You can do this in the windows msconfig boot advanced options option. set the number of processors to less than you have.
This will tell you how sensitive your games are to the benefits of many cores.
If your FPS drops significantly, it is an indicator that your cpu is the limiting factor, and a cpu upgrade is in order.
Unfortunately, your motherboard is not recommended, particularly for overclocking a FX-6 cpu.
Read this:
http://www.tomshardware.com/forum/id-2384024/motherboard-tier-list-970-chipset.html
If you end up needing more individual core speed, Intel of some sort is your real answer.