Rowvacuation homomesy for the type B piecewise-linear statistic

Let $\mathsf{B}^n$ be the type B quotient poset, let $\mathcal{A}^{\mathrm{PL}}_{\kappa}(\mathsf{B}^n)$ denote its $\kappa$-normalized piecewise-linear labelings, and define

$$h^{\mathrm{PL}}_*(\pi) \coloneqq \sum_{\substack{p\in \mathsf{A}^{2n-1},\\ \operatorname{Flip}(p)=p}} \pi(\langle \operatorname{Flip}\rangle p).$$

The type B piecewise-linear homomesy conjecture. The statistic $h^{\mathrm{PL}}_*\colon \mathcal{A}^{\mathrm{PL}}_{\kappa}(\mathsf{B}^n)\to \mathbb{R}$ is $\kappa$-mesic for $\operatorname{Rvac}_{\mathcal{A}}^{\mathrm{PL}}$. This extends the previously established rowvacuation homomesies for the statistics $h^{\mathrm{PL}}_i$; the embedding argument does not establish this additional statistic, so its asserted homomesy remains open.