Bivariate Ehrhart reciprocity conjecture for preorder polytopes

Let $\tau$ be a preorder of size $n$, and let $\mathbb E_\tau(u,v)$ be the double Ehrhart polynomial counting lattice points of the two-parameter polytope $\mathcal Q_\tau(r,s)$. Bivariate Ehrhart reciprocity conjecture.

$$\mathbb E_\tau(-u,-v)=(-1)^n\mathbb E_\tau(u-1,v-1)$$

for every preorder $\tau$ of size $n$. The identity has been verified computationally for all preorders of size at most $5$; the general case remains open.