The bunchy factor conjecture

Let $G$ be a strongly connected graph. A graph is bunchy when, for every state $I'$, the map $\Sigma_G|_{F(I')}:F(I')\to F(\Sigma_G(I'))$ is a bijection. A factor of $G$ is synchronizing if it is obtained from $G$ by a synchronizing right resolver.

Bunchy factor conjecture. Every strongly connected graph has a bunchy synchronizing factor.

If true, every minimal synchronizing factor would be bunchy, and the cited results would imply uniqueness of the synchronizing factor. The source notes that the conjecture is known for almost bunchy graphs and later proves it for bi-resolving graphs, but gives no resolution for all strongly connected graphs.