Sergel's bi-brick-permutation C-expansion conjecture

Let $\mu$ be a partition, and let $\Pi$ range over bi-brick permutations. Associate to each $\Pi$ a partition statistic $\mu(\Pi)$, a composition statistic $\alpha(\Pi)$, and a nonnegative integer statistic $stat(\Pi)$. Let $C_{\alpha}$ denote the creation-operator symmetric function indexed by the composition $\alpha$. Sergel's conjecture. There is a nonnegative integer $stat(\Pi)$ such that

$$(-1)^{|\mu|-l(\mu)}m_{\mu}=\sum_{\mu(\Pi)=\mu}q^{stat(\Pi)}C_{\alpha(\Pi)},$$

where $\mu(\Pi)$ and $\alpha(\Pi)$ are certain statistics of the bi-brick permutation $\Pi$. If true, this would provide a positive $C$-expansion and support the corresponding Schur-positivity conjecture; the supplied text gives no resolution.