The skew shape poset block-statistic conjecture

Let $P$ be a skew shape poset of size $n$, let $S_n(P)$ denote the set of $P$-partitions of the labeling set represented by permutations, and let $\widetilde{bl}_P(\sigma)$ be the number of blocks in the valid block decomposition associated with $(P,\sigma)$. Here $\Omega(P;t)$ is the order polynomial of $P$. Skew shape block-statistic conjecture. For every skew shape poset $P$ of size $n$,

$$n! \, \Omega(P;t)=\sum_{\sigma\in S_n(P)}t^{\widetilde{bl}_P(\sigma)}.$$

This conjecture proposes a combinatorial interpretation of the coefficients of the order polynomial for skew shape posets, extending the corresponding proved formula for fence posets. Its status is not specified in the source.