Single-orbit conjecture for wave-front sets of reductive-group representations

Let $F$ be a non-Archimedean local field, let $\bf G$ be an algebraic reductive group over $F$, and let $G=\bf G(F)$. For $\pi\in\operatorname{Irr}(G)$, let $\operatorname{WF}^{\max}(\pi)$ denote the union of the maximal nilpotent coadjoint $G$-orbits occurring in the closure of the wave-front set of the character of $\pi$. Single-orbit conjecture. For every $\pi\in\operatorname{Irr}(G)$, the set $\operatorname{WF}^{\max}(\pi)$ lies in a single $\mathbf{G}$-orbit. This would give the non-Archimedean analogue of the corresponding multiplicity and wave-front results discussed in the source, including the case associated with the diagonal subgroup. The source gives no evidence resolving the conjecture.