Disconnect the rear sway bar on one end. If ride doesn't change, not the issue.

You are asking for the ride and harshness to improve. High end performance shocks probably aren't going to help. They help control really stiff springs (which you don't have) and control weight transfer. You are trying to make it a little more Cadillac, not make it more Viper.

You are looking to dampen and soften the high speed shock acceleration for noise, vibration, and harshness (NVH). That quick movement comes from bumps, cracks, roughness in the road.

Low speed dampening is the vehicle weight transfer/transition side to side, front to rear, or both (corner to corner)

I'd look at Bilstien RCD. Maybe an adjustable, But it would be just set on the soft settings.