Powerful-tableau formula for chromatic quasisymmetric functions of K-chains

Let $a,b\geq2$ be positive integers, let $\gamma=(a,2,2,\ldots,2,b)$, and let $K_\gamma$ be the corresponding K-chain with associated poset $P$. K-chain powerful-tableau formula conjecture.

$$X_{K_\gamma}(\mathbf{x},q)=\sum_{\lambda\vdash|K_\gamma|}\sum_{T\in\operatorname{powST}_P(\lambda)}q^{\operatorname{inv}_{K_\gamma}(T)}e_\lambda(\mathbf{x}).$$

The conjecture seeks to extend the proved path case to K-chains; the source presents it as motivated by computational experiments.