Ext branching laws for the general linear group

Let F be a non-archimedean local field. Let π₁ and π₂ be irreducible Arthur type representations of GLₙ(F) and GLₙ₋₁(F) respectively. We study Ext branching laws when π₁ and π₂ are products of discrete series representations and their Aubert-Zelevinsky duals. We obtain an Ext analogue of the local non-tempered Gan-Gross-Prasad conjecture in this case.