Usher's obstruction-supremum conjecture for ellipsoid embedding functions

For $n\geq 1$, define

$$L_{n,0}=\sqrt{n^2-1}.$$

Let $A_{k,n}$ and $\hat A_{k,n}$ be Usher's obstruction classes, let $\mu_{\mathbf{E},L_{n,0}}$ denote the obstruction associated to a class $\mathbf{E}$, and let $\mathrm{accum}(L_{n,0})$ be the accumulation point of the infinite staircase for $c_{L_{n,0}}$. Let the center of $A_{0,n}$ be the left endpoint of the interval under consideration.

Usher's conjecture. Between the center of $A_{0,n}$ and $\mathrm{accum}(L_{n,0})$, the function $c_{L_{n,0}}$ equals

$$\sup\{\mu_{\mathbf{E},L_{n,0}}:\mathbf{E}\text{ is one of the }A_{k,n}\text{ or }\hat A_{k,n}\}.$$

Usher proved that $c_{L_{n,0}}$ has an infinite staircase, while this conjecture predicts the complete embedding function up to its accumulation point using the indicated obstruction classes.