Largest-denominator conjecture for semiqueens

Let $F_k$ be the Fibonacci numbers, and let $\mathbb Q^{21}$ denote the semiqueen. For $q$ semiqueens, consider all vertices of the associated inside-out polytope. Semiqueen maximal-denominator conjecture. The largest denominator of a vertex for $q$ semiqueens $\mathbb Q^{21}$ is

$$F_{\lfloor q/2\rfloor}$$

if $q$ is even and

$$F_{\lfloor q/2\rfloor+1}-1$$

if $q$ is odd. This is presented as the specialization of the general three-move maximality conjecture to semiqueens.