Max-minus-min homomesy conjecture for interval-closed sets of products of two chains

Let $P=[m]\times[n]$ be the product of two chains, and let $\mathcal{IC}(P)$ denote its interval-closed sets. Under rowmotion on $\mathcal{IC}(P)$, consider the statistic that assigns to each interval-closed set the number of its maximal elements minus the number of its minimal elements. A statistic is $0$-mesic if its average on every rowmotion orbit is zero. Max-minus-min homomesy conjecture. The number of maximal elements minus the number of minimal elements is $0$-mesic under rowmotion on $\mathcal{IC}(P)$, for $P=[m]\times[n]$.

This conjecture was posed in the cited earlier work; the source notes that the case $m=2$ was already proved there, while the general case remains open.