Jantzen filtration intertwining conjecture for the KZ functor

Let $W$ be a finite real reflection group with rational Cherednik algebra parameter space $\mathfrak{p}$, let $\mathfrak{p}_{\mathbb{R}}$ be its real form, and let $\Delta_c(\lambda)$ be a standard module with irreducible $W$-representation $\lambda$. Fix $x_0\in\mathfrak{h}_{\mathbb{R},\mathrm{reg}}$, and let $KZ_{x_0}$ be the corresponding Knizhnik–Zamolodchikov functor. For a base parameter $c_0\in\mathfrak{p}_{\mathbb{R}}$ and deformation direction $c_1\in\mathfrak{p}_{\mathbb{R}}$, consider the Jantzen filtrations defined by the corresponding families of Hermitian forms. Jantzen filtration intertwining conjecture. For any base parameter $c_0\in\mathfrak{p}_{\mathbb{R}}$ and deformation direction $c_1\in\mathfrak{p}_{\mathbb{R}}$, the functor $KZ_{x_0}$ sends the Jantzen filtration on $\Delta_c(\lambda)$ to the Jantzen filtration on $KZ_{x_0}(\Delta_c(\lambda))$. The first two filtration terms are known to be intertwined; the conjecture asserts this for every term, and the source indicates that either a direct argument or a categorical deformation argument may prove it.