Minimum reflection factorization conjecture for symplectic and minus-type orthogonal groups

Let $G$ be either the finite symplectic group $\operatorname{Sp}_{N}(q)$ or the finite minus-type orthogonal group $\operatorname{O}^{-}_{N}(q)$, and let $c$ be a Singer cycle in $G$, with $N=2n$ even. Let $h:=|c|$ be the multiplicative order of $c$. Minimum reflection factorization conjecture. The number of factorizations of $c$ as a product of the minimum number $N$ of reflections in $G$ is

$$h^{N-1}.$$

This conjecture is motivated by computational exploration and would extend the paper's factorization-counting results to these additional finite groups of Lie type; the source does not indicate that it is resolved.