Rigidbody or Transform Movement

[_Aka_]

Using OffsetRadius or not is I think just a detail. The important thing is to use like you said pseudo gravity and velocity to have a good looking jump. Once you calculated the height using that, you can either apply it by modifying directly the transform, or consider the difference between the desired height and the spline's height, and apply that through the OffsetRadius

FYI, OffsetRadius is used for jumping in example scene 50_EndlessRunner