Suspension travel between stock and aftermarket setup

[cossie1600]

Question guys. I have a set of the giant 295 40 18 Hoosier A6s. Since I am no longer autoxing and they are impossible to sell due to the size, I am going to use it at the track. The only issue I have is that those A6s rubbed slightly (at the top of the fender liner where the plastic comes down), which I assume is from the height of the tire as it is huge and I assume it only happens at full braking or hard turns when it was stock. Since my car is now 1-1.5" lower, but with a much stiffer spring setup, would the suspension give enough travel for it to rub like it did before?

Thanks