In any case, if you ditch the run-flats there is already room for increased stability and grip without loosing the comfort. Perhaps harder springs and softer dampers is the way to go. But it takes an engineer and a good driver to really appreciate and tune such a system.
I have to ask you, why do you want to go faster on the track? Why not just have fun at slower speeds and spend the money on fuel etc instead? You can stiffen the car up, and go a tiny bit faster, but how is it worth it?