For what its worth:
Everyone has been avoiding the sad truth... THESE CARS UNDERSTEER!! its the sad truth about mid engine cars....
There are only a few ways to change this in most mid engine cars...
1) Mass amounts of front negative camber
2) Tire Pressures
3) Tire sizes
4) Suspension...
Most of these have already been touched on, and i know you want to keep your car stock so here we go....
1) This option is out of running, stock suspension will never get you over -1.0 degrees of negative camber in the front, and sadly, this isn't enough
But should defiantly still be done if you're trying to get the best performance/handling out of the car.
2) Again, should still be done but will not magically turn off your understeer... You mentioned running lower tire pressures in the rear. Wrong school of thought. As a rule of thumb, lower pressures means more grip. So if anything run lower pressures in the front. Porsche recommends 29 Front 36 Rear (which is a 7 PSI gap compared to the 5-6 PSI you were thinking about running)
3)Okay here we go. The magic number here is 245s all the way around. They fit in the front, and in the rear. For autocross i've been running 245/40/18 Hoosier A6's all the way around. I know you're not Autocrossing, but its still a good number to run with. Keeps the car very well balanced.
4) Obviously out of the running if you want to keep the car stock.
My '02 S is also bone stock, and seemed to find its happiness after completing the first 3 of these. An aggressive alignment is very needed, and playing with tire pressures really makes you learn your car. After it is closely balance with tires, playing with tire pressures can make you find what your car is actually capable of. However, i have no idea what to recommend for track racing on that front. Maybe ask some one else where to start, or just get out there and try it!!
Good luck!
~Brad
Cheers!