In my experience (admittedly it's with much lighter cars with modified or swapped engines mostly) a LSD often doesn't give you that much more traction it just makes the car more predictable when you lose the grip, I would imagine a heavier car with silly power is much the same.
On mine I'd just like to stop the inside wheel spinning and then the traction control cutting all the power when I'm trying to pull out of a wet junction.
Mine also does this, not sure if the TC turns off at a set speed but this was about 40-45mph, road was damp but the car has the right tyres on with decent tread and it wasn't that cold that day.