[Angelo DiTocco]

Rusty.... don't roll your ride
Most have had to tighten the rear shock settings W/ radials
Radials also need more air than the bias ply, not less, but that's not the whole story.

They are definitely more sensitive to irregularities in the track surface and even subtle inconsistencies in the suspension setup on the car.

For example, check your front end settings, shock settings, wheel travel, and snubber settings.... if they are uneven and you have one tire hitting the ground before the other coming out of a wheel stand .... or .... one side hitting a snubber before the other when you hit the brakes, those mismatches are transfered to the rear suspension and then oscilate from side to side with the radials. You would not even notice it with bias-plys.
I would check that stuff first, since it is in the shutdown area where the issues arise. Does it start immediately after you lift off the gas, or does it start when you apply the brakes? That's important to know.

I've seen some of the hemi cars rock the whole way down the track when one front wheel lands before the other after the wheelstand.

What weight do you run the car at?
What rear springs do you have?
What brand & size radial?