reallly that video is far too short to see what the car's true behaviour is. Start of the race, I assume on cold tyres, and maybe on and off the gas running at close quarters with the other cars in Turn 1. The only real issue seemed to happen in the middle of the 1st turn. Exiting that turn and all through turn 2 was just smooth consistent oversteer. Turn 3 is a non event. Turn 4 you get loose on entry trailing the brake a bit, but I don't see the oscillation after that. But whatever causes the oscillation evident in turn 1, it's not the absence of a panhard bar.

my first question is about your old tyres. just how old are they? You could be chasing a suspension problem that doesn't actually exist.

did it stay the same through the whole race, or get better/worse?

has it always handled like this? or just started displaying this problem?

did you do the full competition suspension manual setup with traction arm and sway bar?

The diff moving laterally under load is not an issue in itself. Any leaf spring setup without lateral location will do that. My old 1200 used to do it noticably. It won't cause this loading and unloading unless something else is now making it bind, like a traction rod or a swaybar clamped to the springs...