Errors when sweeping with a projected sketch?

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I'm working on a simple ball model that will end up looking a bit like one of those hand-juicers, but with twisted edges and smooth (not as sharp) indentations :
Here's what I've got so far. I made a sphere, drew a spline the length of the sphere, projected the spline onto the sphere, removed one half of the projection, then rotated a copy of the half to create a "slice" of the sphere.
From there I wanted to sweep a semicircle profile using the two projected splines, which would cut into the sphere, then circular pattern this sweep 6 times around the sphere to get even cuts. However, when I tried sweeping, I got error messages about the sweep intersecting itself, illegal surfaces, and the path not being smooth:
I feel like my understanding of how the sweep tool and 3D sketches work are not correct, or there could've been a better workflow for what I'm trying to accomplish; if so, what would be a better way to go about what I'm trying to do? Also, how do you add elements to 3D sketches? I find that when I go to constrain elements such as sketch profiles or splines starting from the ground plane (such as the circle profile above), I can only snap one side at a time using a coincident constraint, leaving the other side still on the 2D plane and therefore completely warping the element.
File: https://a360.co/2HtnMjS