Hi ticket-spite,
I'm unaware that one could disconnect the content from the timeline and have real-time working while also asking to srub back the timeline that holds keyframes for the whole execution.
This sounds more like something for game engines, and Cinema 4D is not one of them by default.
One more thought: Things will get more complicated when the Spline is a curve. If it is only a straight direction, P.X., for example, why use a spline?
The next question would be, how do you define acceleration? It is typically not a linear process. So, defining that by time needs a formula that also expresses this curve-like behavior.
I think that there is an option. Still, you might check in the Developer Café, as you like to do something that needs to store a lot of data to mark the actual starting time, then calculate what happens with the time points you mentioned and have the real-time representing it on the screen, while refreshing and played needs to be ignored.
https://developers.maxon.net/?page_id=1114
In the Q&A forum, my reply is: Bake it as Alembic, and bake again when changes are needed. But no, Alembic is not time-independent.
A tip for the XPresso setup: Sort the XManager from top to bottom in how the information flows. Otherwise, you might have a priority issue at one point.
What Cinema 4D is built is an animation system that targets the rendering results. Check Unreal or Unity for those needed extended options.
My best wishes for your project
