JC,
Pretty open ended question that I hesitate to post advice about.
I really don't want to talk to someone who put their car in a wall trying to do something I posted about online.
Please be careful out there. These are $50k street cars you are using at a DE event.
The best advice I can give you is to go to a professional driving school (Skip Barber, Jim Russell, etc). I have been to three driving schools and several of the shorter follow on versions.
My cautions noted for the record,

, I read your question not as one of oversteer, or one of braking for a turn, but a situation where you are just past turn in, not to the apex, and realize you have too much speed to make the arc of the turn without exiting the track at the exit.
So you have come down the straight and finished braking, turned in and heading for the apex thinking... mmmm, this is a little fast for me..., what to do....
Feather the throttle. Not a big lift which unweights the rear and leads to big oversteer, but a slight lift to slow the car down and transfer weight forward. Feathering will either help reduce understeer and allow you to reduce the arc of the turn, or... lead to some oversteer which you should be ready for, depending on how your car is set up. The Z06 understeers naturally, but not much. Large lifting will induce oversteer.
But feathering and slowing will allow you to carve a tighter arc. On a long sweeper, you may need to stay feathered all the way to the exit of the turn to stay on the track.
If you do carry too much speed to the exit and drop two wheels off (assuming there isn't a wall there), DON'T PANIC. Don't jerk the car back on the track, you'll likely spin to inside in that case. Ease off the throttle, keep the car straight and gradually bring it back on the track.
A couple other thoughts for you.
- As was said above, look where you want to go, not where you don't want to go. Your hands will instinctively steer the car to where your eyes are looking. Train your eyes to look down the track, not at the wall, the tires, the spinning car in front of you...
- Comp Mode works well on the track. If you are using comp mode, steer the car where you want to go. If comp mode senses you are too fast, it will apply individual brakes as necessary to keep the car on that arc. It won't save you from the really stupid, but if you are close, it will work.
