Specialization of the polymatroid invariant to Speyer's invariant

Let ${\mathcal G}$ be the invariant of polymatroids defined in the paper, and let $g_{\bf X}(t)$ be Speyer's invariant of a matroid ${\bf X}$. Specialization conjecture. The invariant ${\mathcal G}$ specializes to Speyer's invariant. The supplied text introduces Speyer's invariant and records this expected specialization, but gives no proof or resolution.