DSXDH-shape conjecture

Let $G$ be a definite Gross inner form, let $\mathcal{M}(G)$ be the set of $A$-shapes, and let $h(G,\varsigma;q)$ be the counting function defined from discrete global $A$-parameters and their packet multiplicities. Let $X_{\mathfrak{p}}(q)$ be the associated congruence complex. DSXDH-shape conjecture. Fix a finite prime $\mathfrak{p}$. Then for any $\varsigma\in\mathcal{M}(G)$,

$$h(G,\varsigma;q)\ll|X_{\mathfrak{p}}(q)|^{\frac{2}{r(\varsigma)}}.$$

This is the definite Gross inner form analogue of the CSXDH-shape conjecture; the source gives no evidence of resolution.