Ring-generation conjecture for shifted plactic skew Schur $P$-functions

Let $\lambda/\mu$ be a shifted skew shape, and let $\mathcal{P}_{\lambda/\mu}$ denote the shifted plactic skew Schur $P$-function of shape $\lambda/\mu$. The shifted plactic Schur $P$-functions are the corresponding functions indexed by straight shifted shapes.

Ring-generation conjecture. $\mathcal{P}_{\lambda/\mu}$ belongs to the ring generated by the shifted plactic Schur $P$-functions.

This asserts that skew shifted plactic Schur $P$-functions can be expressed using the ring generated by their straight-shape counterparts. The supplied text gives no evidence resolving the claim, so its status remains open.