Symplectic singularities conjecture for modified complex symplectic quotients

Let $(V,G)$ be a representation of a compact Lie group $G$, with complex moment map $cmu$ and real quotient $M_0$. Define the modified complex symplectic quotient to be the complexification of the real quotient,

$$\operatorname{Spec}\big(\mathbb{R}[M_0]\otimes_{\mathbb{R}}\mathbb{C}\big).$$

Symplectic singularities conjecture. For all $(V,G)$, the modified complex symplectic quotient has symplectic singularities and is graded Gorenstein.

This modifies the usual complex symplectic quotient in cases where $(V,G)$ fails to be $1$-large, by taking the real radical before complexifying. The claim is proposed as a generalization of the theorem for $3$-large representations, but the source indicates that proving it will require different techniques.