How about making it much simpler than that?
Having had my fair share of racing discussions with drivers I supported as a mechanic or photographer, I'm familiar with Ideal-Line, which is an optimal path along a racetrack. One goes a little bit on the opposite side first to widen the curve radius, then gently breaks more and more and tightens the radius while accelerating, leaving the curve.
Below is a simplified version of that. But it is the fastest version. Just the swinging that one might expect. Note that cars do the opposite, while the driver often counters that move with the head. So it is a discussion of what view is provided. Motorcycles do the opposite. So, I understand that the ideas about this are split.
If the opposite is needed, drag the blue Spline below and adjust the camera accordingly.
I have copied one of the Splines that describe the path and set it to B-Spline while placing it higher.
This is used in a new Camera Rig as a Rail Path (Tangential is on).
The Interpolation "Number" for all splines has been increased to 24 points to make it smoother.
I have placed a cube as a child on the camera to showcase the new motion more clearly. This object can be deleted.
Adjust the 'blue" Spline as needed.
My best wishes for your project
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