The pmaj refinement of the generalized Delta conjecture

Let $m,n,k$ be in the range for which $\mathsf{PLD}(m,n)^{\ast k}$ is defined, and let $\mathsf{pmaj}(D)$ denote the proposed partial-major-index statistic on a partially labelled Dyck path $D$. The pmaj conjecture.

$$\Delta_{h_m}\Delta'_{e_{n-k-1}}e_n=\sum_{D\in\mathsf{PLD}(m,n)^{\ast k}}q^{\mathsf{area}(D)}t^{\mathsf{pmaj}(D)}x^D.$$

The source reports only computer verification and a few supporting special cases. Thus the proposed refinement remains open.