Friedman–Hyttinen–Weinstein generalized Borel-reducibility main gap problem

Let $\mathcal T_1$ be a classifiable theory and $\mathcal T_2$ a non-classifiable theory. A generalized Borel-reducibility main gap problem. asks whether there is a Borel reduction from the isomorphism relation of $\mathcal T_1$ to the isomorphism relation of $\mathcal T_2$. This asks for a generalized descriptive-set-theoretic counterpart of Shelah's main gap theorem; the supplied source does not state whether the problem has been resolved.