Mizuno's duality conjecture for modular Nahm quadruples

Let $D=\operatorname{diag}(d_1,\dots,d_r)$ with $d_1,\dots,d_r\in\mathbb{Z}_{>0}$, let $A\in\mathbb{Q}^{r\times r}$ be symmetrizable with symmetrizer $D$, meaning that $AD$ is symmetric positive definite, let $B\in\mathbb{Q}^r$, and let $C\in\mathbb{Q}$. If the generalized Nahm sum associated with $(A,B,C,D)$ is modular, call $(A,B,C,D)$ a modular quadruple. Define

$$A^\star=A^{-1},\qquad B^\star=A^{-1}B,\qquad C^\star=\frac{1}{2}B^\mathrm{T}(AD)^{-1}B-\frac{\operatorname{tr}D}{24}-c,\qquad D^\star=D.$$

Mizuno's duality conjecture. If $(A,B,C,D)$ is a modular quadruple, then $(A^\star,B^\star,C^\star,D^\star)$ is also a modular quadruple.

This generalizes Zagier's proposed duality from Nahm triples to symmetrizable matrices and generalized Nahm sums. The source attributes the conjecture to Mizuno; the supplied material gives no resolution, so its status is recorded as open.