Conjectural splitting of the virtual class for twisted maps to the universal root stack

Let $X$ be a smooth pair with boundary divisor $D$, let $r$ be a positive integer, and let $\Lambda$ denote the discrete data of the twisted maps. Write $\mathrm{Orb}_{\Lambda}(\mathcal{A}_r)$ for the corresponding moduli space of maps to the universal $r$-th root stack, let $\mathrm{vd}$ be its virtual dimension, and let $Z_{[\tau],\Gamma'}$ be strata indexed by types $[\tau]$ and graphs $\Gamma'$. For each stratum, let $a_{[\tau],\Gamma'}$ be a coefficient and let $C_{[\tau],\Gamma'}$ be a Chow class depending on $r$. Conjectural splitting. There exists an expression

$$[\mathrm{Orb}_{\Lambda}(\mathcal{A}_r)]^{\mathrm{vir}} = \sum_{([\tau], \Gamma')} a_{[\tau], \Gamma'} [Z_{[\tau], \Gamma'}] \cap C_{[\tau], \Gamma'}$$

where the sum is over strata of dimension at least $\mathrm{vd}$ and $C_{[\tau],\Gamma'}$ is a Chow class which is a Laurent polynomial in $r$ such that

$$\operatorname{deg}_r([Z_{[\tau], \Gamma'}]) + \operatorname{deg}_r(C_{[\tau], \Gamma'}) \geq 0.$$

This proposed decomposition is intended to provide the general structure of the virtual class needed to deduce the polynomiality results for twisted maps to smooth pairs. The source gives no resolution of the conjecture, so its status remains open.