Tom,
I run urethane (polyurethane) in all the suspension bushes, front and rear.
I'll scan the shock dyno and send it though after work.
It seems to me the car doesn't want to settle on turnin. What we can't see from the video is if you are correcting the issue or adding to it via steering input.

On a side note, maybe something to generate some discussion and something Ive been thinking about lately.
In roll, is there a sensible limit to the amount of rear body roll with leaf spring cars? Should total rear roll angle be a key setup value for racing with leaf springs.
If the tyres generate more lateral g (as they do in modern entry racing e.g A032 v A050s), this would change the required rear roll stiffness to limit roll angle. In turn this is balanced with a change in front roll stiffness.