The conjecture that reflexive simplices have no ML degree drops

Let $\Delta$ be a reflexive simplex, and let $\mathrm{mldeg}(\Delta)$ and $\mathrm{deg}(\Delta)$ denote its maximum likelihood degree and degree, respectively, under the standard scaling. Reflexive-simplex ML degree conjecture. Reflexive simplices do not exhibit ML degree drops with the standard scaling; that is,

$$\mathrm{mldeg}(\Delta)=\mathrm{deg}(\Delta).$$

The computations in the paper verify equality for several explicitly constructed families and their first instances, but no general proof is given.