Determinantal q-Eulerian conjecture for reverse plane partitions of thickened zigzag strips

Let $\delta_n$ denote the staircase shape, let $\operatorname{RPP}(\delta_{n+2k}/\delta_n)$ be the reverse plane partitions of the skew shape $\delta_{n+2k}/\delta_n$, and let $E_k^*(q)$ be the relevant $q$-Eulerian polynomial. Define

$$\widetilde{E}_k^*(q)=\frac{E_k^*(q)}{(1-q)\cdots(1-q^k)}$$

and $N=k(k-1)(6n+8k-1)/6$. Determinantal q-Eulerian conjecture.

$$\sum_{\pi\in\operatorname{RPP}(\delta_{n+2k}/\delta_n)}q^{|\pi|}=q^{-N}\det\left[\widetilde{E}_{2(n+i+j)-3}^*(q)\right]_{i,j=1}^k.$$

This is proposed as an analogue of the preceding determinant formula for the corresponding generating function, and is supported only by preliminary computations in the supplied text.