Non-degeneracy conjecture for adjoints of generic polygonal Wachspress models

Let $Q=B^T\cdot P_b$ be a generic $n$-gon, and let $\alpha_Q$ denote its adjoint polynomial. A Laurent polynomial is non-degenerate with respect to its Newton polytope when its face polynomials define smooth hypersurfaces in the corresponding algebraic tori.

Adjoint non-degeneracy conjecture. For a generic $n$-gon $Q=B^T\cdot P_b$, the adjoint $\alpha_Q$ is non-degenerate, with Newton polytope equal to the Newton polytope of

$$(1+y_1+y_2)^{n-3}.$$

This conjecture is the geometric input for the predicted maximum-likelihood-degree formula of the Wachspress model. The source gives no proof or resolution.