First of all, take your limit-pushing to the race track or autocross course. I guess I don't care if you wreck your car or kill yourself, but you might take someone else out with you.
It sounds like you're entering the corner hot enough to scare yourself, so you're getting off the throttle. This will transfer weight to the front end, and can cause the back end to come around (this is called trailing-throttle oversteer).
With your listed mods, the car should tend towards understeer if you're not doing something dumb like jumping off the gas mid-corner or trailing the brakes in way too far. Get your braking done earlier so you're coming into the corner at a little safer speed, and start getting on the gas sooner. The car will be more stable, you'll be less likely to upset it and send it twirling into the woods, and you'll learn a technique that will allow you to get around a corner a lot more quickly. Since my car is set up right on the ragged edge of oversteer, I'll try to get almost all of my braking done before I point the car into the turn. As soon as I hit the apex of the turn, I'm back into the throttle and trying to get down the next straight as quickly as possible. Going into the corner too quickly screws up my ability to get back into the throttle, and makes the car less stable - going slower and increasing the chance of swapping ends is not the way to pull down good lap times.
The most important point is still my first one - don't dick around with exploring your traction limits on the street.