Speyer covering conjecture for Gaudin monodromy

Let $\overline{M_{0,n+1}}(\mathbb{R})$ carry Speyer's covering and the covering constructed in the source, denoted the source's covering from Corollary~. Speyer covering conjecture. These two coverings are isomorphic. The conjecture is motivated by the common Schubert-calculus description of their generic fibers; the source notes connections with $GL_N$-crystals and Etingof's conjecture.