The LERF conjecture for non-Seifert-separated 3-manifolds

Let $N$ be a compact, orientable, irreducible $3$-manifold with empty or toroidal boundary. Suppose no torus of the JSJ decomposition bounds a Seifert fibered $3$-manifold on both sides. LERF conjecture. The group $\pi_1(N)$ is LERF. This would extend known separability results beyond hyperbolic and geometric graph-manifold cases; the source gives no resolution status.