That Control Spline issue looks like what the Original Poster was encountering.
I kinda know why, Control Splines are NURBS Curve. Fit Spline is more like Bezier Curve.
AI and Affinity Designer don’t have built in NURBS Curve so it looks like it’s converting it to segmented curves with high resolution.
So as far as I know only software that can convert Control Spline Correctly is RHINO to PDF. If others have better conversion method, please post.