Please excuse my denseness, but why dont they(ring particles) float in a cloud as opposed to being in a disc?
I would think that unless there is some preferential gravity effect around the equator(of a sphere!) that they would be randomly distributed.
A "sphere" as you've described it consists of many orbits which intersect one another. Particles on such orbits eventually collide; the result of such collisions is that the sphere eventually "averages out" into a ring or disk, in which setup (you will note) none of the particle orbits intersect any more.