Unfortunately, you can't really do much better on your current FM2+ mobo. A worthwhile CPU upgrade really requires a new motherboard, with all modern motherboards also requiring DDR4. $200 is not enough for that... You could possible do a bare minimum Pentium, ultra cheap mobo and bare minimum RAM for $200, but that's kind of a side-grade, depending on the game.
While the A10s are hardly the best, I'm a bit surprised you're seeing an "extreme" bottleneck. Which games are you seeing that in? What's the GPU utilisation while you're playing (use GPU-Z or similar to monitor).