Unique projective crepant resolution for Type II quiver varieties

Let $\root\in\Sig$ be a dimension vector of Type $\II$, and let the associated quiver variety be the variety determined by this dimension vector. Type II uniqueness conjecture. If $\root\in\Sig$ is a dimension vector of Type $\II$, then the associated quiver variety has a unique projective crepant resolution. The conjecture is motivated by computations in which the number of chambers in the secondary arrangement agrees with the size of the Namikawa Weyl group; the supplied text gives no resolution or counterexample.