Antichain-indicator symmetry conjecture for odd uniform self-dual fences

Let $a$ be a positive integer, let $t$ be odd, and let $F=\breve{F}(a^t)$ be the uniform self-dual fence with $t$ segments. For $i\in\{1,\ldots,t-1\}$, let $s_i$ and $s_{t-i}$ be the corresponding shared elements, and let $\chi_{s_i}$ and $\chi_{s_{t-i}}$ be their antichain indicator statistics. Antichain symmetry conjecture. For every $i\in\{1,\ldots,t-1\}$, the statistic

$$\chi_{s_i}-\chi_{s_{t-i}}$$

is 0-mesic under rowmotion.

The authors state that this stronger conjecture was confirmed computationally for $a+t\leq 10$, for $F=\breve{F}(2^9)$, and for $F=\breve{F}(8^3)$.