Realization of small ML degrees for the triple Segre product

Fix an integer $d\leq n$. Let $w=(w_{ijk})$ be a scaling for the Segre embedding of $\mathbb P^1\times\mathbb P^1\times\mathbb P^{n-1}$, defined by

$$w_{ijk}=\begin{cases}1 & \text{if } k>d\text{ or }i=1,\\ k & \text{if } k\leq d\text{ and }i=2.\end{cases}$$

Small-ML-degree realization conjecture. The resulting scaled Segre embedding has ML degree $d$. This gives a proposed construction realizing every degree in the indicated range; the general construction is presented as conjectural.