The quasiharmonic deformation conjecture for singular vectors

Let $W$ be a real reflection group with reflection representation $V$, let $H(W)$ be the universal rational Cherednik algebra, and let $\mathcal{QH}\subset H(W)$ be the space of universal quasiharmonics. For a parameter $c$, write $M^{(c)}(\mathbf{1})$ for the polynomial representation, call a vector singular if it is annihilated by all Dunkl operators, and write $\operatorname{ev}_c\mathcal{QH}$ for the specialization at $c$. Quasiharmonic deformation conjecture. For every singular function $c$, all the singular vectors of $M^{(c)}(\mathbf{1})$ belong to

$$\operatorname{ev}_c\mathcal{QH}.$$

Equivalently, the space of singular vectors in $M^{(c)}(\mathbf{1})$ should be deformable within the class of quasiharmonics. The conjecture is proved for dihedral groups in the cases described by the source, while computations for symmetric groups support it; the general statement remains open.