The rise-decorated rectangular shuffle conjecture

For $m,n\in\mathbb{N}$, let $e_{m,n}$ be the rectangular symmetric function, let $\Theta_{e_k}$ be the theta operator indexed by $e_k$, and let $\mathsf{LRD}(m+k,n+k)^{\ast k}$ denote rise-decorated labeled rectangular Dyck paths of size $(m+k)\times(n+k)$. Rise-decorated rectangular shuffle conjecture.

$$\left.\Theta_{e_k}e_{m,n}\right\rvert_{q=1}=\sum_{\pi\in\mathsf{LRD}(m+k,n+k)^{\ast k}}t^{\mathsf{area}(\pi)}x^\pi.$$

The conjecture is attributed to Iraci, Pagaria, Paolini and Vanden Wyngaerd. The problem of finding a $\mathsf{dinv}$ statistic for rise-decorated paths remains open.