Is there a way to make 180 x-axis movement look smoother on Cinemachine?

I love Cinemachine so far!
I have a FreeLook camera with binding "Lock To Target On Assign", and I have a script that makes player rotation affected by camera rotation.

Code (CSharp):

1. moveDirection = (Quaternion.AngleAxis(cameraTransform.rotation.eulerAngles.y, Vector3.up) * moveDirection).normalized;

Anyway, the only issue I am having is that when my character does a sudden 180 turn on x-axis, the Camera looks like it 'jolts' to instantly shift with it.

Gif of this:
https://i.imgur.com/qn6lFDz.mp4

Turning on "Horizontal Damping" for each Rig works for this, but is there a way to create this damping behavior via script? Because I will only need to turn on that damping for the circumstance of player doing quick keypress, but otherwise will not want the damping on that high.
Otherwise is there an alternative recommended solution?
Thanks!