Conjectural skew Littlewood–Richardson rule for Schur Q-functions

Let $\lambda,\mu,\sigma,\tau$ be partitions and fix a tableau $T$ of shape $\tau$. For skew tableaux, write $|S^-|$ for the number of entries in $S^-$, and let $S^-*S^+*S$ denote their product under the tableau operation $*$.

Conjectural skew Littlewood–Richardson rule. The product of skew Schur $Q$-functions should satisfy

$$Q_{\mu/\lambda}\cdot Q_{\tau/\sigma}=\sum (-1)^{|S^-|}Q_{\mu^+/\lambda^-},$$

where the sum is over triples $(S^-,S^+,S)$ of skew tableaux of respective shapes $(\lambda/\lambda^-)$, $\mu^+/\mu$, and $\sigma$ such that $S^-*S^+*S\equiv_{\textsc{sp}}T$.

This conjecture is a reformulation of the preceding skew Littlewood–Richardson theorem, replacing the shifted jeu-de-taquin equivalence by Serrano's shifted plactic equivalence. It gives a direct combinatorial rule for products of skew Schur $Q$-functions, while its status is not resolved in the supplied source context.