I have the Kazz 1.5 on the 370 and can confirm their is no lurch or pitch, it just digs in and launches you out of corners, it is though more noisy on tight turns.
Episode 3 Tamsin Greg goes around with TC on but to be fair i think she would probably have killed herself without it ! BUT the the queen of the ring does an amazing lap on her home turf in the new Golf GTI clubsport.
The standard 370 GT diff cover is flat(ish) only the Nismo has the finned cover standard as far as i am aware and as i have a Kazz LSD and it gets blooming hot on track days this is a way of keeping temps a bit lower, it also holds more oil.