Equality conjecture for the strongly Ricci-negative cone

Let $\mathfrak{n}$ be a nilpotent Lie algebra, let $\mathfrak{t}(\mathfrak{n})$ be a maximal torus of diagonalizable derivations, let $\mathfrak{t}(\mathfrak{n})_{\mathrm{srn}}$ be the strongly Ricci-negative cone, and let $\operatorname{Cone}(\mathfrak{n})$ be the open convex cone defined using the moment-map construction in the source. Equality conjecture.

$$\operatorname{Cone}(\mathfrak{n})=\mathfrak{t}(\mathfrak{n})_{\mathrm{srn}}.$$

The proposition preceding this conjecture establishes only the inclusions $\mathfrak{t}(\mathfrak{n})_{\mathrm{srn}}\cap\mathfrak{t}(\mathfrak{n})_{\mathrm{gen}}\subset\operatorname{Cone}(\mathfrak{n})\subset\mathfrak{t}(\mathfrak{n})_{\mathrm{srn}}$; equality is therefore the remaining question.