It seems to occur while accelerating hard out of turns. LSD, tires slipping on the rim, brakes? I don't know, but it only happens on R comps. I thought it was just the tires rubbing on something, but after watching the vid I don't think that's the case and I couldn't find any evidence of it.

2012 dixie tour Sunday - YouTube

 

What year is your car? Do you have stability control?

Could be stability control applying braking force to inside wheel to keep you from spinning? Whenever my stability kicks in over the winter it sounds like the ABS kicking in although its braking a single wheel.

If it was the tires you would think you would here the sound as soon as the car dives into a corner, the sound seems to be coming mid corner most times.

@ 1:04 you can also hear the moan speed up with the car so IDK just a thought.

 

Should have put that in the op, but it's an 09.' I turn the ESC off, but your post makes me wander if it still has some authority...

 

Could it be a bad bearing?

Or maybe your shafts if your lowered.

 

I read that our LSD makes a low whining noise

I get that noise when I autocross in rain

skip to 1:27 for that noise

UBC SCC 2011 Slush Series 2 Autocross - YouTube