Period-denominator equality for two-move rider chess-piece configurations

Let $u_\mathbb{P}(q;n)$ be the counting quasipolynomial for nonattacking configurations of $q$ copies of a two-move rider $\mathbb{P}$ on the dilated unit board, and let $D([0,1]^{2q},\mathcal{A}_\mathbb{P}^q)$ be the denominator of the associated inside-out polytope. The period of $u_\mathbb{P}(q;n)$ is the shortest length of its cyclic sequence of constituent polynomials. Period-denominator equality conjecture. The period of the counting quasipolynomial $u_\mathbb{P}(q;n)$ equals the denominator

$$D([0,1]^{2q},\mathcal{A}_\mathbb{P}^q).$$

The period always divides the denominator by Ehrhart theory, but equality is generally surprising because periods can be smaller than denominators; this conjecture asserts equality for these chess-piece counting quasipolynomials.