The way I would approach this is make whole spheres into the shapes I want first go through scaling in one direction and showing points on the sphere then stretching the points around to suit. I would have the triangle above the spheres and scale with the spheres. I would then cut with the triangles and then boolean it all together and then remove the bottom. That way you can make all of your decisions while they are sphere shapes and everything after that is just simple labor. if that makes sense.