Shifted bar tableau formulas for connective Schur functions

Let $\beta$ be a parameter, let $\beta$-dependent skew functions $j\hspace{-0.2mm}p_{\nu}$ and $j\hspace{-0.2mm}q_{\nu}$ be indexed by strict partitions, and let $\mu\subseteq\lambda$ be strict partitions. A shifted bar tableau of shape $\lambda/\mu$ is a pair $(V,\Pi)$ consisting of a semistandard shifted tableau $V$ and a partition $\Pi$ of its boxes into adjacent same-entry bars; let ${\rm ShBT}_Q(\lambda/\mu)$ be the set of all such tableaux and ${\rm ShBT}_P(\lambda/\mu)$ the subset whose underlying tableau has no primed diagonal entries. For $T=(V,\Pi)$, write $|T|=|\Pi|$ and $x^T$ for the monomial recording the entries of its blocks. Shifted bar tableau conjecture. If $\mu\subseteq\lambda$ are strict partitions, then

$$j\hspace{-0.2mm}p_{\lambda/\mu}=\sum_{T\in {\rm ShBT}_P(\lambda/\mu)}(-\beta)^{|\lambda/\mu|-|T|}x^T,$$

and

$$j\hspace{-0.2mm}q_{\lambda/\mu}=\sum_{T\in {\rm ShBT}_Q(\lambda/\mu)}(-\beta)^{|\lambda/\mu|-|T|}x^T.$$

The formula is presented as a new conjectural generating function and the source gives no resolution evidence; the authors note that proving it would suffice to handle the case $\mu=\emptyset$.