Morita equivalence conjecture for generalized Schur algebras and RoCK blocks

Let $\mathcal B$ be a weight $d$ RoCK block of the usual $q$-Schur algebra $S_q(N,f)_\mathbb F$, with quantum characteristic $e>0$. Let $\ell=e-1$, and let $Z$ be the corresponding extended zigzag algebra. For $n\geq d$, consider the generalized Schur algebra $T^{Z}_{\mathfrak z}(n,d)$. Morita equivalence conjecture. The algebra $T^{Z}_{\mathfrak z}(n,d)$ is Morita equivalent to $\mathcal B$. This proposes a Morita equivalence between the generalized Schur algebra associated with the extended zigzag algebra and every weight $d$ RoCK block. The supplied text gives no resolution evidence, so the conjecture remains open in this record.