Unfortunately, different quantum spin orientations don't appear to evade the weak equivalence principle. Dropping Bose-Einstein condensates in vacuum drop towers is a popular experiment. An example, "Tests of the Universality of Free Fall with Atoms in Different Spin Orientations", 2016, <http://dx.doi.org/10.1103/PhysRevLett.117.023001> which is the published version of <https://arxiv.org/abs/1503.00433v1>. Likewise, one would not expect a ferromagnet and a ferroic glass to fall differently in a drop tower.

Quantum spin is relevant in post-Newtonian (GR-compatible) gravitation, though.

Rough argument: let's represent perturbations of the metric (gravitational waves) as a massless spin-2 boson field on top of some sourceless background geometry; this is essentially the programme of perturbative quantum gravity. (’t Hooft, <https://dspace.library.uu.nl/bitstream/1874/4708/2/16331.pdf> corresponding to DOI10.1142/9789812796653 (_0007).) This is almost General Relativity. GR's "no prior geometry" (MTW §17.6) axiom puts paid to the idea of obtaining a compatible theory by inserting some force into a static background, and ultimately this idea that spacetime is dynamic is what causes PQG to be a poor theory for strong gravitational interactions ('t Hooft ut supra, 2nd paragraph of §4).

Spin-2 interactions are attractive for the same charge. As far as we know, physicality demands PQG treat everything (including the gravitons) in the universe as possessing the same sign of gravitational charge. We can't (quasi-)neutralize with matter or vast collections of gravitons, so we can't charge screen in the sense of <https://en.wikipedia.org/wiki/Electric-field_screening> as opposed to having things like Lagrange points in Newtonian gravitation.

There is a family of theoretical approaches involves appreciable amounts of matter with opposite gravitational charges from everything else or introducing two "opposite" metrics and coupling most matter to our familiar one and a minority of matter to the other. Informally, we make gravitational and inertial masses unequal for some matter, breaking the weak equivalence principle (unlike in my first paragraph). Evidence takes us away from these approaches.

Additionally, opposite rank-2 tensor charges repel, so it's hard to imagine engineering up a scheme that uses any "anti-gravitating" matter with a single metric tensor, and theoreticians would have to imagine some cutoff to prevent runaway acceleration of an anti-gravitating particle let loose inside the solar system; Bondi, 1957, <https://doi.org/10.1103/RevModPhys.29.423>

One sketch of this sort of idea off the top of my head is Hossenfelder's "Antigravitation", <https://arxiv.org/abs/gr-qc/0508013>, which is per the author a toy idea (each Standard Model particle has a gravitational-anti particle) that makes a simplifying assumption that takes one away from general curved spacetimes (ibid., §4 and the para below eq. 17, which is suggestive of Bondi's runaway).

Instead, we might try to contrive a universe with a complement of fun things like pp-waves (which maybe one can get with your spheres and rings). It's unlikely that this can be done without going outside the limits of linearized gravity (GEM and so forth), and such exotic things tend to cause gravitational collapses. (E.g. Bondi & Pirani XIII <https://royalsocietypublishing.org/doi/10.1098/rspa.1989.001...> aka <https://doi.org/10.1098/rspa.1989.0016> which is on scy hob if you need that) Because of B&P, it occurs to me that if we have a line of galaxies in an expanding Robertson-Walker spacetime, perturbing that with a caustic wave might keep (the remnants of) the galaxies from exiting each others' Hubble volumes, which maybe you can sort of think of as effective FTL, or perhaps related to the "FTL" of the most distant galaxies disappearing from view).

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Universality of free fall / Galilean gravity treat: https://en.wikipedia.org/wiki/File:Apollo_15_feather_and_ham...