I always look at the things you draw and have no Idea how your going to complete the task, you always find an answer! After your first drawing I thought you where going to draw a 3d spline on the outside of the sphere and intersect the points, Either way I'm always lost and amazed at your teaching.
You want the pipe to self-intersect? For that you need make a pipe section for each tu. Split the face of the surface body and do multiple pipe sections.
I've made a jewelry component like that by making two flat spirals out of a piece of wire. One spiral is wound the opposite direction of the other. The end the wire in each spiral is pulled up to create each half of the sphere and then the two halves are twisted in such a way as to create the sphere made of a spiral. My description isn't the greatest and I can't find the exact video I originally watched to learn the technique. This video shows how to do it with a round stone captured inside the sphere: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-2YNagDsIxao.html&pp=ygUZc3BpcmFsIHdpcmUgYmFsbCBlYXJyaW5ncw%3D%3D I really enjoy your videos.