Pointed-collection conjecture for finite quotients of tame fundamental groups

Let $M_{g,n}^{\rm ord}$ be the ordinary moduli space, let $q_{\rm gen}$ be its generic point, and let $\pi_A^{\rm t}(q)$ denote the set of finite quotients associated with the tame fundamental group at $q$. For each closed point $t$, define $\mathcal{C}_t=\{G\in\pi_A^{\rm t}(q_{\rm gen})\mid t\in U_G\}$, and let $\mathscr{C}_q$ be the set of pointed collections contained in $\pi_A^{\rm t}(q)$. Pointed-collection conjecture. For each $t\in M_{g,n}^{\rm ord,cl}$, $\mathcal{C}_t$ is a pointed collection; moreover, for every $q\in M_{g,n}^{\rm ord}$, the natural map

$${\rm colle}_{q}:\mathscr{V}_{q}^{\rm cl}\longrightarrow\mathscr{C}_{q},\qquad [t]\longmapsto\mathcal{C}_{t},$$

where $\mathscr{V}_{q}^{\rm cl}:=V_q^{\rm cl}/\sim_{fe}$, is a bijection. The conjecture is intended to reconstruct group-theoretically the finite quotients of closed points of $V_q$ from $\pi_A^{\rm t}(q)$, but the source gives no resolution.