The intersection of a cylinder and a plane is an ellipse.
The intersection of torus and plane is a toric section.
I think that your smaller ring is NOT a torus.???
So make the smaller ring by revolving a circle?

I need more study:-)

Brian

Or, per Michael, slant lengths are different, in different places, by the geometry.

Conversely, if equal slant lengths are the goal, the inner ring would have to be modified,
To be squished down to an undulating "ellipsoid" (or toric section?), cross section?