Tautologicality of the Tor class of the product locus

Let $\mathcal M_g^{\leq 1}$ be the moduli space of stable curves of genus $g$ with degenerations of torus rank at most $1$, and let $\overline{\mathcal A_1 \times \mathcal A_{g-1}}$ denote the closure of the product locus in the corresponding partial compactification of the moduli space of principally polarized abelian varieties. Write $\operatorname{Tor}^*$ for the Tor-class construction associated with this locus. Tautologicality conjecture. The class

$$\operatorname{Tor}^*([\overline{\mathcal A_1 \times \mathcal A_{g-1}}])$$

lies in the tautological ring $R^*(\mathcal M_g^{\leq 1})$. This is motivated by the computation of the analogous Tor class as a tautological class on the moduli space of compact-type curves; whether the stated class is tautological on $\mathcal M_g^{\leq 1}$ remains open.