De-equivariantized generalized Haagerup modular data for mixed even parts

Let $A$ be an abelian group with $A_e\cong\mathbb{Z}_{2^n}\times\mathbb{Z}_2$ for $n\geq2$. Mixed-even-part conjecture. The modular data of the Drinfeld center of the $\mathbb{Z}_2$-de-equivariantization are given by the stated data with $G=\mathbb{Z}_{2^n}^2\times A_o\times\widehat{A_o}$, $q_{1,e}(x,y)=\zeta_{2^n}^{xy}$, and $q_{1,o}(a,\chi)=\chi(a)$; the modular data of the original center are the corresponding tensor product with the quadratic form $Q(x,y)=(-1)^{xy}$. The claim is open beyond the examples in the source.