Vanishing conjecture for stable-pairs descendents of holomorphic $(p,0)$-classes

Let $X$ be a simply-connected smooth projective 3-fold, let $\gamma\in H^{p,0}(X)$ with $p=2$ or $p=3$, and let $D\in\mathbb D_{\textup{PT}}^{X}$. For $k\geq 0$, the stable-pairs descendent invariant $\left\langle\textup{ch}_k(\gamma)D\right\rangle_{n,\beta}^{X,\textup{PT}}$ is defined by integration over the virtual class. Vanishing conjecture. For every $k\geq 0$, $n\in\mathbb Z$, and $\beta\in H_2(X;\mathbb Z)$,

$$\left\langle\textup{ch}_k(\gamma)D\right\rangle_{n,\beta}^{X,\textup{PT}}=0.$$

This vanishing is presented as a consequence of the stable-pairs Virasoro conjecture: the class $\textup{ch}_2(\gamma)$ vanishes, and the Virasoro relations would force all the displayed descendents to vanish. Since the underlying Virasoro conjecture is open in this generality, this consequence is also open.