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If you put the 305 ET Street S/S on the car then you shouldn't be having that big of a problem.
However I know people that hate Mickey drag radials for that exact reason (Big end sway). Friend of mine put 20" drag radials on his Vette wheels, we took it out for a ride, did like 120 and when he let off, the car changed a lane by itself, literally. We went home and changed the tires.
If you can't get it resolved, then I highly advise switching to a NT05R. Slightly stiffer sidewall, slightly less launch, but more stability in all circumstances. At least that's what us local car group guys have deduced.
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