I would suggest AD08's as having more traction than PSS's.
The RS3's have better hot traction than AD08's on a track, but are worse than AD08's if they are not hot or if it is cold or wet out.
Agree with 11 inch rims, a E92, and maybe a littler negative chamber you could fit a 305/30/19 on the rear.
2011 e92 M3 Monte Carlo Blue ESS 535 - gone but not forgotten
2015 cayman GTS - new toy
2006 SLK 55 AMG sold