I think your best bet here might be to build that profile into the shape that you intersected in the first place. How did you build the curved shape that you started with, which extension? Could you build a bottom face with the spine arc flattened by 2M?
If you were to turn that into a wedge shape with thickness along the spine before intersecting with the x,y plane cutting shape, the result would be what you are looking for. If you are intersecting 3D shapes then you would really benefit from using solid tools. I did this quick demo using Eneroth solid tools.
