What i mean by you cant drive it with the ESP on is, it refuses to let the rear end play meaning you can't key the front in or adjust the car on the throttle to hold the best line, then it will not let you open the throttle early enough to power out of the bend effectively. It turns a 182 Cup into a Clio.
At no point before this had you managed anything about driving on track,so I would assume this is you driving on the road,so don't be a Bellend.
And I would still say that a LSD is not really needed,even if doing a few track days.Like everything,it all helps but the car can be moved along at a fair old pace without one.