Uniqueness of the predominant orientation type for accordion graphs

Let $G$ be an $(n,v,d)$-accordion graph. An orientation type is non-vanishing when its coefficient in the associated graph polynomial is nonzero, and predominance is with respect to the dominance order on orientation types. Define

$$\Lambda(n,v,d)=(0^v d^v\cdots [(n-2)d]^v [(n-1)d]^v).$$

Predominant orientation-type conjecture. The partition $\Lambda(n,v,d)$ is predominant among all non-vanishing orientation types of $G$.

The source proves that $\Lambda(n,v,d)$ is a maximal orientation type and that it is non-vanishing, but notes that dominance is only a partial order and gives no proof that it is the unique non-vanishing maximal type; the conjecture therefore remains open.