Ok, I bet you bought a Full LSD right? If not, you should. But I bet you took it and cranked all of the LSD values to the highest, thinking it would increase traction right?
Put all of the front LSD values for the front very low i.e. 10 for a 1,000hp Skyline.
Put the rear initial torque to 15
Put the rear Accel to 30
Put the rear decel to 20
Try this out, the lower the value of the LSD the longer the wheels can spin independantly of each other. This will help you turn, and then the LSD will kick in and let you accelerate nicely. For the decel, having it low will make the car more responsive to turn in under braking, but you might notice a very minimal drop in braking distance.
But either way, you should see your lap times go down.
Normally, I dont drive or recommend 1,000hp cars. They suck.
I dont usually go over 650hp unless it is a very balanced car. i.e. Ruf RGT is one of the few cars that should have that much hp.
But a Skyline is generally pretty tame with a shade over 600hp.
A Supra shouldnt have much more than 550hp, or you will be spending too much time keeping it under control, rather than practicing driving techniques and staying on the line.