I don't believe that you would need separate cores to achieve an "ellipsoidal shape" as long as the deepness of the feature is parallel to the casting molding separation direction. The thin wall between the ellipsoidal shapes as well as the lack of radius blends are problematic.
Be aware that it may not be necessary to achieve the final geometry with sand cast. As-cast geometries are commonly post-machined to achieve un-castable geometries, mechanical tolerances, etc..
Have you consulted your casting manufacturing job shopper or equivalent professional?