Flippa, other than learning how to handle a 500hp car, the Corvette oversteer problem (the car spinning out on the turns) could be corrected by putting an extreme understeer tuning on your Corvette. For example, buy the racing springs, then tune them like this:
This is an severe understeer setup, which should
help eliminate the oversteer/spinout problems you have.
Of course, now you have a new set of problems with a severe understeer setup. With understeer, you will have to slow down more before a turn, otherwise you'll just slide off the track (only now you will slide front tires first, instead of rear tires first). Also, with your front springs that stiff, it will be difficult to steer on bumps because the front tires will have less contact with the ground. And if you do end up on the grass, you will find that getting the car back onto the track can be troublesome, as your steering will be hindered due to your front wheels having less contact, as you rumble off-road. You will also get a little surprise once in a while, when you turn the steering wheel and almost nothing happens as your understeer is so severe.
Now what you do is gradually soften the front springs to take away the understeer and bring the car into a better balance. You should soften the springs little by little until just a bit of the oversteer returns, and then adjust your driving technique to correct it (or just put the front springs a pinch stiffer again).
Keep in mind, you can also soften the rear springs instead of stiffening the front springs, to create an understeer effect.
I enjoy a car with a slight understeer, as I like slowing down a bit more before the turn, and mashing the gas after a turn, rather than riding into a turn faster and having to wait longer to get back on the gas. (supposedly Jeff Gordon and Jimmy Johnson enjoy a slight understeer in their racecars as well)