Strange Duality morphisms conjecture for moduli spaces on abelian surfaces

Let $A$ be the abelian surface and let $v$ and $w$ be Mukai vectors satisfying Assumptions and, with the associated moduli spaces and determinant line bundles as in the paper. Denote the three strange duality morphisms by $\mathsf{SD}^{+}$, $\mathsf{SD}^{-}$ and $\mathsf{SD}$. Strange Duality morphisms conjecture. When Assumptions and are satisfied, the three morphisms

$$\mathsf{SD}^{+},\mathsf{SD}^{-},\mathsf{SD}$$

are either isomorphisms or zero. This is a speculation concerning the expected behavior of strange duality in the stated numerical setting; the supplied text does not establish the assertion or indicate a resolution.