Graded extension conjecture for generalized Asaeda–Haagerup categories

Let generalized Asaeda–Haagerup categories be de-equivariantizations of generalized Haagerup categories for the groups $\mathbb{Z}_{4m}\times\mathbb{Z}_2$ with $\epsilon_{(0,1)}$ trivial. Graded extension conjecture. Similar $\mathbb{Z}_2\times\mathbb{Z}_2$-graded extensions exist for generalized Asaeda–Haagerup categories. This extends the exhibited extensions of the Asaeda–Haagerup fusion categories to the generalized family; the supplied source gives no resolution of the claim.