Finiteness conjecture for tight contact structures on atoroidal 3-manifolds

Let $M$ be a closed, connected, irreducible 3-manifold. It is atoroidal if it does not contain an incompressible torus.

Finiteness conjecture. If $M$ is atoroidal, then $M$ carries only finitely many isotopy classes of tight contact structures.

This is presented as the flip side of the theorem asserting infinitely many universally tight contact structures on closed, connected, irreducible 3-manifolds containing an incompressible torus. The source does not provide evidence that the finiteness claim has been resolved.