Morales's Ehrhart positivity conjecture for CRY and Tesler matrix polytopes

For $\boldsymbol{a}\in\mathbb{N}^n$, let $\operatorname{Tes}_n(\boldsymbol{a})$ be the polytope of upper triangular $n\times n$ matrices with nonnegative entries and hook sum $\boldsymbol{a}$. Define the CRY polytope by

$$\mathcal{CRY}_n=\operatorname{Tes}_n(1,0,\dots,0),$$

and call $\operatorname{Tes}_n(1,1,\dots,1)$ the Tesler matrix polytope. Morales's conjecture. For each $n$, the CRY polytope $\mathcal{CRY}_n$ and the Tesler matrix polytope $\operatorname{Tes}_n(1,1,\dots,1)$ are both Ehrhart positive. These polytopes arise from Tesler matrices and include the Chan--Robbins--Yuen polytope, whose volume formula is known. The positivity assertion is based on computations for small $n$ and remains open in the supplied source.