I may be wrong, but I don't think you've actually driven a car that handles. If you think the GTO is a neutral handling vehicle, you're flat out insane.
It's not a great drift car, the power steering can't react quick enough to back and forth movements, and the LSD makes tight, low speed maneuvers damn near impossible. It's frustrating at an autocross coming out of a low speed corner, getting back in the throttle, and having the inside wheel go up in smoke.
When driven hard in an autocross setting, or even road course duties, it has a tendency to push... bad! It has an enormous amount of body roll, which is actually very suprising to me. The brakes suck, you can't stop, and they get hot fast. You really can't expect a 4000lb car to handle like a lotus though!
As far as modifying the suspension, there are finally some aftermarket pieces coming out that are pretty decent. I know Koni makes a nice shock now, BMR, Hotchkis, and others make sway bars, sub-frame connectors and the like. But I think this site is mostly dedicated to the drag racer, and the car show type guys, which is fine!
I'm not hating here at all, but I do know I'm behind the 8-ball trying to get my car nationally competitive in SCCA competition. I have a set of Hawk pads waiting to be installed, I will be purchasing race tires this week or next (Kumho V710 ofcourse) and I am looking at the HAL shocks that Tbyrne has... though he hasn't shot me a price yet!
Anyways, I suggest getting a new set of tires for your car, and a set of Koni shocks. It will be a start to a good handling car!