Unimodality conjecture for statistics on separable permutations

Let $S_n$ be the set of separable permutations of length $n$, and for $\pi\in S_n$ let $\operatorname{lmax}(\pi)$, $\operatorname{rmax}(\pi)$, $\operatorname{lmin}(\pi)$, and $\operatorname{rmin}(\pi)$ denote the numbers of left-to-right maxima, right-to-left maxima, left-to-right minima, and right-to-left minima, respectively. For a statistic $\operatorname{stat}$ in this set, consider the distribution of the number of permutations with $\operatorname{stat}(\pi)=k$. Unimodality conjecture. The distribution of separable permutations $\pi\in S_n$ with $\operatorname{stat}(\pi)=k$, $\operatorname{stat}\in\{\operatorname{lmax},\operatorname{rmax},\operatorname{lmin},\operatorname{rmin}\}$, is unimodal with the peak being at $k=2$ for $n\geq 3$. The conjecture is based on computational data and suggested embeddings between classes of separable permutations; a combinatorial proof remains open.