Baking a slider driven curve from Grasshopper so it exists as a dynamic/animated curve purely within Rhino

I have a Grasshopper definition that generates a curve and the coordinates of the curve’s points are controlled by a slider.

The end result of what I’m trying to achieve is an animated curve/spline that I can import into a separate 3D program (in this case Cinema4D).

I’ve tried using LunchBox/Object Bake to bake sequential curves out but this is not a viable solution given my workflow beyond exporting from Rhino (amongst other things I need to be able to re time the animation once in Cinema 4D and morphing between the sequence of curves does not function correctly).

I can import Rhino files into Cinema4D using the Rhino IO plugin but it will not import anything that is being generated from Grasshopper.
I figure that if I can convert the animated curve generated from Grasshopper into a singular animated curve that exists within Rhino with no Grasshopper dependencies then this will work - but I’m not sure how to do this.

Any ideas greatly appreciated!