Hi Ed,
I dont have a solution for the boolean, I think Michael has provided that, but I wanted to show you the method I used to create the sine wave on your ring using one segment curve.

I used Isect to get points on the surface that I could snap to with the draw curve through points tool. If there are enough control points it will follow a surface pretty well. For your sine with less frequency, I would have had to add radial to my circle array to get my points going in the sine curve to get enough to keep the curve on the surface.

FYI



With this file I can acheive the boolean with sweep arcs at .019 and .02. So I think thats MoI's Tolerance of .001 you would be hitting. But that leaves quite an awful looking intersection area when zoomed on a computer, but may not be noticable on a small detail ring. May even create some kind of unique sheen.

Also...3d printing??? If so, I understand. If it's cnc, no need to create the solid in this manner. Care to elaborate?

Burr