Ext-vanishing conjecture for standard Whittaker sheaves

Let $x$ be a point of the curve, let $\Whit_x^\kappa$ be the metaplectic Whittaker category at $x$, and let $\mathcal F_{x,\mu}$ denote the Whittaker object indexed by a dominant coweight $\mu$. If $\mu<\mu'$ are dominant coweights and their difference is not a simple coroot, then Ext-vanishing conjecture.

$$\operatorname{Ext}^1(\mathcal F_{x,\mu},\mathcal F_{x,\mu'})=0$$

in $\operatorname{Whit}_x^\kappa$. This is presented as a reformulation-inspired expectation following the equivalence with the subtop cohomology property; the supplied text gives no evidence that it has been proved or disproved.