I don't think you can control AVX current specifically, but here is what helps me to keep AVX load under control. Since, as you mentioned, AVX load draw substantially more, the power a CPU consumes also increases. Now, you can control the total power cap under CPU Power Management menu item. Set Long duration power Limit to some number that is above your normal full load and less then AVX full load. Then CPU will be told to jump to a lower P-state to conform to this power cap.
In my case, this is 150 and then AVX heavy benchmarks make the CPU drop from 5.1 to some 4.5-4.6 and I see the power stays quasy-constant at 150W
But I have way higher voltages then you, so you should really select your own cap value.