Strong Ext relevance conjecture for non-tempered Arthur representations

Let $F$ be a non-archimedean local field. Let $\pi_1$ and $\pi_2$ be Arthur type representations of $\operatorname{GL}_n(F)$ and $\operatorname{GL}_{n-1}(F)$, respectively. Say that they are strongly Ext relevant when they satisfy the decomposition condition in the paper's definition, namely when there exist Speh representations whose products and highest-derivative factors express $\pi_1$ and $\pi_2$ in the prescribed paired form. Strong Ext relevance conjecture. If $\pi_1$ and $\pi_2$ are strong Ext relevant, then

$$\operatorname{Ext}^i_{\operatorname{GL}_{n-1}(F)}(\pi_1,\pi_2)\neq 0$$

for some integer $i\geq 0$. This conjecture proposes strong Ext relevance as a sufficient condition for nontrivial Ext branching in the non-tempered Arthur-type setting; the source does not state a resolution.