ED-degree formula conjecture for Schubert varieties

Let $1\leq i<j\leq n$, and let $\mathcal{S}_{ij}$ be the Schubert variety in ${\rm Gr}(2,n)$. ED-degree conjecture. If $i<j-1$, then

$$\operatorname{EDdegree}(\mathcal{S}_{ij})=2(n-j+1)^2(j-i)-(n-j+1)(n-i).$$

The formula was verified in the paper for $n\leq12$ by Gröbner-basis computations over finite fields and for $n=13,14$ using homotopy continuation, but remains conjectural in general.