Circular orderability conjecture for rational homology sphere graph manifolds

Let $W$ be a rational homology sphere graph manifold. Circular orderability conjecture. If $\pi_1(W)$ is infinite, then $\pi_1(W)$ is circularly orderable. The conjecture isolates the remaining difficult graph-manifold cases, especially those with two Seifert fibred pieces admitting finite fillings. A general slope-detection theory for circular orderings is suggested as a possible way to prove it, but the claim remains open.