Sokal's factorial monomial-positivity conjecture for products of elementary symmetric functions

Let $\lambda=(\lambda_1,\dots,\lambda_n)$ and $\mu=(\mu_1,\dots,\mu_n)$ be partitions with at most $n$ parts satisfying $\mu\subseteq\lambda$. Let $k$ and $r$ be integers with $0\leq r\leq k-1$, and let $\mathbf{x}^{(1)},\dots,\mathbf{x}^{(k)}$ be variable sequences. Sokal's conjecture. The determinant

$$\det\left(\left((\lambda_i-\mu_j-i+j)!\right)^r e_{\lambda_i-\mu_j-i+j}(\mathbf{x}^{(1)})\cdots e_{\lambda_i-\mu_j-i+j}(\mathbf{x}^{(k)})\right)_{i,j=1}^{n}$$

is $m$-positive, meaning that it is a nonnegative integer combination of monomial symmetric functions in the relevant variable sets. This conjecture strengthens Schur's theorem on factorial Hadamard products of real-rooted polynomials and extends Sokal's Hadamard-product conjecture. The source does not state whether it has been resolved.