Never done autocross myself but with my 'not a S30' Z for circuit laps and tight corners the following driving technique shows promise, where it suits to have any braking completed prior to using the technique.
Come in a bit fast, back off momentarily on the throttle at the same time turning the wheel firmly into the corner, get back on the throttle immediately the car has turned in and drive out of the corner with as much throttle as possible.
The idea is to turn the car in quickly while the extra weight due to the throttle backoff transfer is on the front wheels. For faster corners trail braking may also help by holding extra weight over the front wheels while turning in.
Using weight transfer to get the car doing what you want is very satisfying as a driver, particularly when you don't get it right very often like me