Orientation in 2D

[_Aka_]

I learned that you can't instantiate and rotate a control point in the same step since there are some functions (GetOrientationFast) that needs the cache from the spline.

This is no more the case. Methods that add control points to a spline now make sure that the spline cache is up to date. Which version of Curvy do you use?

What has me struggling is that even when I try to set all the control point orientations to a fixed rotation, they still get twisted into 3D on some curves at run-time.

Either set your spline's orientation to Static, or if you wan to keep it as Dynamic, set to true the Orientation Anchor value for the control points which rotation you define.