Maximal non-Gorenstein locus conjecture for symmetric orbit closures

Let $Y_{\gamma}$ be an orbit closure, and let $\operatorname{Maxsing}(Y_{\gamma})$ be the set of Bruhat-maximal orbits along which $Y_{\gamma}$ is singular. Let $\operatorname{MaxnonGor}(Y_{\gamma})$ be the set of Bruhat-maximal orbits along which $Y_{\gamma}$ is non-Gorenstein. Maximal non-Gorenstein locus conjecture.

$$\operatorname{MaxnonGor}(Y_{\gamma})\subseteq\operatorname{Maxsing}(Y_{\gamma}).$$

Equivalently, a maximal non-Gorenstein orbit should be a maximal singular orbit. The source explains the motivation and reports verification for all $(p,q)$ with $p+q\leq 7$ and many cases of $(p,q)=(4,4)$; the general statement remains open.