Finite vertical-strip expansion formula for shifted stable Grothendieck polynomials

Let $\mu$ be a strict partition. For strict partitions $\lambda\supseteq\mu$ with $\ell(\lambda)=\ell(\mu)$, let $\textsf{SD}_{\lambda/\mu}$ be the shifted skew diagram. A vertical strip is a subset of $\mathbb{Z}_{>0}\times\mathbb{Z}_{>0}$ containing at most one position in each row, and let $c(\lambda/\mu)$ be the number of distinct columns occupied by positions in $\textsf{SD}_{\lambda/\mu}$. Vertical-strip expansion conjecture. Then

$$G\hspace{-0.2mm}Q^{(\beta)}_\mu=2^{\ell(\mu)}\cdot\sum_{\lambda}(-1)^{c(\lambda/\mu)}\cdot(-\beta/2)^{|\lambda/\mu|}\cdot G\hspace{-0.2mm}P^{(\beta)}_\lambda,$$

where the sum is over the finite set of such strict partitions $\lambda$ for which $\textsf{SD}_{\lambda/\mu}$ is a vertical strip. The source reports that computer calculations suggest this finite formula and gives it as the ensuing conjectural description of the expansion.