The factor-free valley square conjecture

For $n,k\in\mathbb{N}$, let $\Theta_{e_k}$, $\nabla$, and $\omega$ be the indicated symmetric-function operators, let $p_n$ be the power-sum symmetric function, and let $\mathsf{LRP}'(n+k,n+k)^{\bullet k}$ be the subset of valley-decorated labeled square paths in which the bottom-most vertical step lying on the base diagonal is not decorated. Factor-free valley square conjecture.

$$\Theta_{e_k}\nabla\omega(p_n)=\sum_{\pi\in\mathsf{LRP}'(n+k,n+k)^{\bullet k}}q^{\mathsf{dinv}(\pi)}t^{\mathsf{area}(\pi)}x^\pi.$$

The source emphasizes that this version has no multiplicative factor, but gives no resolution; it remains open here.