If I may, larger diameter tires don't necessarily provide more traction. It would depend on the precise use as to what tire to go to. If road racing, softer compound (r type, with a wear rating or less than 100) and wider dimension if possible. Stay with a low sidewall for reduced tire flex in corners.
If drag racing, then softer compound, like a drag radial, but a tire with as much side wall as possible. A 40 to 60 side wall height will provide the ability to lower air pressure, get the sidewall to flex, and allow for much, much greater traction at launch.
Another good addition, that I have mentioned before, but been shot down hardily on, is the dreaded and weak-kneed traction control.
Seems like a necessary addition at the place where many of our cars are. But many think that only neophytes and sissies would ever consider such a device.