Vertical flip duality conjecture for W-superalgebra cosets

Let $N,n,m\in\mathbb{Z}$ satisfy $N>n,m\geq2$, and define $k^\sharp=-k-N+n+m$ and $\ell^\sharp=-\ell-N+n+m$. Let $\operatorname{Com}(A,B)$ denote the commutant of $A$ in $B$. Vertical flip duality conjecture. For generic levels satisfying

$$(k+n-N)(\ell+m-N)=1,$$

there is an isomorphism of vertex superalgebras

$$\operatorname{Com}\left(V^{k^\sharp}(\mathfrak{gl}_m),\mathcal{W}^k(\mathfrak{sl}_{n|N},f_{n|1^m,N-m})\right)\simeq\operatorname{Com}\left(V^{\ell^\sharp}(\mathfrak{gl}_n),\mathcal{W}^{\ell}(\mathfrak{sl}_{m|N},f_{m|1^n,N-n})\right).$$

This predicts equality of the two W-superalgebra cosets obtained from the two resolutions of the conifold diagram under vertical flip.