Intermediate-Jacobian non-isomorphism conjecture for quartic double solids and GM threefolds

Let $Y$ be a quartic double solid and let $X$ be a GM threefold. Let $J(Y)$ and $J(X)$ denote their intermediate Jacobians, each with its principal polarization. Intermediate-Jacobian non-isomorphism conjecture. The principally polarized abelian varieties $J(Y)$ and $J(X)$ are not isomorphic. This conjecture is proposed as a consequence suggested by the birational-geometric discussion; the supplied text gives no resolution.