Infinite-dimensionality conjecture for Besse metrics on spherical 2-orbifolds

Let $G<\operatorname{O}(3)$, and consider the spherical $2$-orbifold $S^2/G$. The real projective plane is covered by $S^2/G$ precisely when $-1\in G$.

The infinite-dimensionality conjecture. If $-1\notin G$, then the moduli space of Besse metrics on $S^2/G$ is infinite-dimensional.

Beyond the known constructions on certain spherical $2$-orbifolds, the source presents this as a conjecture motivated by Guillemin's construction of non-round Besse metrics on $2$-spheres. Its general status is not resolved in the supplied text.