I would go back to street radials.
Most driver makes mistake on just putting slicks on stock car thinking added grip will give much faster lap time.(without thinking how much stress you will be putting on the car)
Although slick tires gives addtional grip/traction, you also need alignment/upgraded bushings/chassis to take full potential of the tires.
Without proper setup, it will only help very marginally on lap time but at sametime it DOES increase much stress on chassis/bushings.(can be worse thing on E93 due to weaker chassis)
Not only that, slick tires give too much confidence to drivers...harder to control at the limit, which is not a good thing for most weekend track drivers.
Any M3 can be very good weekend car even at stock configuration.
Only thing I would change for track are...Brake pads and fluid for fade resistance.
Jusy my $0.02
Jae