Torsen LSD (not Quaife)
Better/Taller tires (225/50 KDW or P03, 17's?)
Poly or 94A Roll Resistors
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I have that problem any time above 1/2 throttle in 1st and 3/4 throttle in 2nd. Just lights up both tires. (though mine pulls straight as an arrow

)
In 3rd there is only a brief hint of wheel spin and only if I intentionally try by punching it from cruise to full throttle above 4500rpm or hard shifting into 3rd which I actually do try to avoid.