The relative hyperbolicity conjecture for atoroidal acylindrical PD3 pairs

Let $(G,\mathbf S)$ be an atoroidal and acylindrical $it{PD}^3$ pair.

Relative hyperbolicity conjecture. The group $G$ is hyperbolic relative to $\mathbf S$.

This is posed as the first of two more precise questions refining Kropholler's geometrisation conjecture. The source mentions related work of Kapovich and Kleiner on $it{PD}^3$ groups acting geometrically on CAT(0) spaces, but does not state a resolution of this relative-hyperbolicity claim.