You and many others on this blog have very good intuition and feeling about the nature of physical reality, but often have difficulty conveying those notions to others.
First of all there are classical notions and quantum notions and there is nothing illogical about either classical or quantum notions, they are simply different. Right now, neither classical nor quantum notions adequately explains all of reality even though both classical and quantum predictions are very good in their limited realms.
A classical spinning sphere is a great analog, but you must be careful and differentiate between a gravity sphere and a charge sphere. And then you must be careful about the observer since a classical observer only perturbs rotation in ways that are knowable and causal. A quantum observer also has knowable perturbations, but a quantum observer perturbs rotation in ways that are not knowable and so are not causal.
A gravity sphere can rotate one way or the other, that is true, and those rotation senses only have meaning relative to the observer. So there are as you say two equal and opposite momentum states and a continuum of states in between. Furthermore, gravity rotation couples with the spin of orbital motion and a rotating sphere that orbits another body will have two very different states in that rotation with and against the orbit phase.
However there is no self energy for a rotating gravity sphere. The spin of a gravity sphere does not affect the gravity of the sphere. But there are all kinds of tidal forces that heat the gravity sphere and the radiation of that heat slows both spin and orbit.
Why this is an elephant in the room completely escapes me.
A charge sphere like an electron can rotate one way or the other as well and that spin magnetism will couple with the magnetism of an electron in orbit around a nucleus. This means that there will be a difference for up spin versus down spin just like a spinning gravity sphere.
A charge sphere in orbit around another charge behaves similar to the gravity sphere and classically, there are a continuum of states. However, the classical charge sphere radiates continuously as it orbits and so loses energy. A quantum electron also radiates, but the nucleus captures that radiation in a resonance that is what quantum is and returns it back to the electron in a perpetual game of catch.
Instead of a continuum of classical states, there are now just discrete quantum states. The electron can be either up or down and the orbit can be a ground state or any number of excited states, each with a factor of two less velocity. In order for the electron to leave, it must lose a succession of discrete photons each a factor of four less in energy in an infinity of Zeno's paradox.
The quantum spin state exists as a superposition of up and down both prior to and in orbit. Unlike the classical spin in a classical orbit, the quantum spin exists in a spherical or S state and there is no up or down yet and no elephant in the room. However, there is a photon of energy lost when a nucleus captures an electron and that photon phase is entangled with the electron spin phase.
So now there is a quantum elephant in the room. The electron also does not exist only in the ground state and spends some short time in all of the states and in fact, the electron spends some time in all of the universe as well. This makes quantum sense but does not make classical sense. Moreover, the electron spin does affect its charge and the electron motion in its orbit also affects its charge. The electron self energy is called the anomalous gyromagnetic ratio and it is possible to derive it from the fine structure constant.
Thus far there is no gravity analog to this effect of spinning quantum charge and its entanglement with the lost photon that literally does exist in the whole universe and that is the elephant that is in the room. With a quantum gravity, of course, there is an analogous self energy and meaning for photon entanglement but that is a different story.
