I've seen this mentioned a number of times - I don't believe there are any "counter-rotating" current rings in the orbitsphere. If there were, then those rings would tend to cancel each other's net angular momentum in the z-axis. But from Israelsson's proof mentioned earlier, we know that 1/2 h_bar is the maximum allowed - ergo there must not be any counter-rotating rings otherwise you could find a covering that increased the net angular momentum beyond 1/2 h_bar.
Since angular momentum is linear in a vector 3-space, you can describe an ensemble of angular momentum from geodesics as a vector summation of projections onto the orthonormal basis set of vectors - i.e. the unit vectors along the x, y and z-axes. Nothing magical about this - just saying that in order to get a uniform covering described by Israelsson and with the boundary condition set by the S-G, one of these axes (the z-axis by convention) will exhibit 1/2 h_bar, while the other two will have +/- 1/4 h_bar.
NB: I'm still not able to post links, but as a reminder, Israelsson's proof can be found at Stack Exchange by searching for "maximal principle uniform covering of a sphere with uniform geodesics".