Semiprimitive local action finiteness conjecture for tree groups

Let $T_d$ be the $d$-regular tree, let $\Omega$ be a finite set, and let $F\leq\operatorname{Sym}(\Omega)$ be semiprimitive, meaning that every normal subgroup of $F$ is either transitive or semiregular on $\Omega$. Consider discrete subgroups of $\operatorname{Aut}(T_d)$ which locally act like $F$ and contain an involutive inversion. Semiprimitive local action finiteness conjecture. There are only finitely many conjugacy classes of such subgroups. The conjecture is presented as the converse to a necessary condition proved by Potočnik, Spiga, and Verret; the source mentions partial results but gives no resolution of this strengthened formulation.