Unimodality conjecture for the two-variable Shi distance enumerator

Let $\mathsf{Dist}_n(k,\ell)$ denote the number of regions of the Shi hyperplane arrangement having the statistics indexed by $k$ and $\ell$. For fixed $n$ and $k$, consider the sequence obtained by varying $\ell$.

Unimodality conjecture. For fixed $n,k$, the numbers $\mathsf{Dist}_n(k,\ell)$ as $\ell$ increases are unimodal.

This conjecture concerns the coefficient distribution of the two-variable refinement of the Shi arrangement's distance enumerator. The supplied text does not state whether the conjecture is known or resolved.