Ishii's maximal-resolution conjecture for quotient surface resolutions

Let $G\subset GL_2({\mathbb{C}})$ be any finite subgroup, and let $X$ be a resolution of $\mathbb{C}^2/G$. Let $Y$ be the maximal resolution of the pair $(\mathbb{C}^2/G,B)$, where $B$ is the boundary divisor determined by the quotient. Ishii's conjecture. The resolution $X$ is dominated by $Y$ if and only if

$$X\cong M_{\theta}$$

for some generic $\theta\in\Theta(G)$. This extends the Craw--Ishii conjecture from the crepant to the non-crepant setting; the formulation concerns which resolutions arise as moduli spaces of stable representations, while the status of the conjecture is not specified in the source.