Unimodality conjecture for higher dimer-cover rank generating functions

Let $\mathcal{G}$ be the snake graph and let $P(\mathcal{G}^*)$ be the associated poset; write $U_{P(\mathcal{G}^*);m}(q)$ for the rank generating function of $m$-dimer covers. Higher dimer-cover unimodality conjecture. The generating function

$$U_{P(\mathcal{G}^*);m}(q)$$

is unimodal. Unimodality is known for ordinary dimer covers, corresponding to $m=1$, but the claim for higher $m$ is presented as a conjectural extension.