The Delta square conjecture in the fall version

For $n,k\in\mathbb{N}$ with $n>0$, let $\Theta_{e_k}$, $\nabla$, and $\omega$ be the indicated symmetric-function operators, let $p_n$ be the power-sum symmetric function, and let $\mathsf{LRP}(n+k,n+k)_{\ast k}$ denote the relevant fall-decorated labeled square paths of size $n+k$. Delta square conjecture, fall version.

$$\Theta_{e_k}\nabla\omega(p_n)=\sum_{\pi\in\mathsf{LRP}(n+k,n+k)_{\ast k}}q^{\mathsf{dinv}(\pi)}t^{\mathsf{area}(\pi)}x^\pi.$$

The source says this is suggested by computer experiments and presents it as a fall-decorated alternative; its status is unresolved in the supplied text.