Hi Vijen6, did the 2002 S have PSM (Porsche Stability Management)?
What are your tire pressures? Maybe 1/2 pound to 1 pound pressure adjustments can help you get more bite. Start with 31-32 up-front and 35-37 in the rear. Make 1/2 pound adjustments, lower, in the rear, and see if that makes an improvement.
I don't think your Falkin tires are Porsche approved. Maybe not a good idea to run 2 different tire types either.
You should participate in some Autocross or DE events with your local PCA and improve your driving skills too. This is not a slam on you, so please don't misinterpret my suggestion. In fact, I need to do this some day too!