Maximal-minus-minimal homomesy conjecture for 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. Rowmotion acts on $\mathcal{IC}(P)$. For an interval-closed set, consider the statistic given by the number of maximal elements minus the number of minimal elements. A statistic is $0$-mesic if its average over every rowmotion orbit is zero.

Maximal-minus-minimal homomesy conjecture. The number of maximal elements minus the number of minimal elements is $0$-mesic under rowmotion on $\mathcal{IC}(P)$ for $P=[m]\times[n]$.

The conjecture was tested on all products of two chains with $m+n\leq 12$. The paper notes that the analogous statistic is not homomesic for the products $[2]\times[2]\times[5]$ and $[2]\times[2]\times[2]\times[2]$, while the conjecture for two chains remains open.