Hi Pior,

re:
> As if I am not mistaken, even using the top Cplane as target seems to require some object
> on the floor to project to

When you use the project to cplane option in the Project command, the cplane is used as the target and no other target object is required.

For example with this 3D curve and no other objects:



Then running the Construct > Curve > Project command and clicking the "Use CPlane" button will result in this projection onto the construction plane, no other objects are involved:



- Michael