I just added another appendix to my page on cubic interpolation of quaternions, with an explanation of how to prevent overshooting using Monotone Cubic Interpolation:

https://theorangeduck.com/page/cubic-interpolation-quaternions#overshoot

Taken from this fantastic blog post (https://jbrd.github.io/2020/12/27/monotone-cubic-interpolation.html) by James Bird