Hopefully Robert (redline) continues to weigh in, he's definitely THE EXPERT in this area... his shop has 2-3 porsche cup cars in it on any given day and he spent years as a mech with PMNA
My thought is that it sounds like you need to work the suspension, this likely isn't a problem with tire pressure based on your cold psi... more negative camber plus stiffen it up... spc/spl control arms plus hotchkis/stillen bars should do the trick... if you decide you want more, then stiffer springs or coilovers... or just keep burning through tires !
