Euclidean distance degree conjectures for resectioning varieties

For generic configurations of points, let $\mathcal{R}_n^{N,h}$ denote the corresponding resectioning variety, and let $\mathrm{EDD}$ denote Euclidean distance degree. Resectioning EDD conjectures.

$$\begin{aligned} \mathrm{EDD}(\mathcal{R}_n^{1,1})&=3n-8 && (n\ge4),\\ \mathrm{EDD}(\mathcal{R}_n^{2,2})&=12n^2-84n+147 && (n\ge5),\\ \mathrm{EDD}(\mathcal{R}_n^{2,1})&=\frac{15}{2}n^2-\frac{115}{2}n+108 && (n\ge6),\\ \mathrm{EDD}(\mathcal{R}_n^{3,3})&=\frac{88}{3}n^3-400n^2+\frac{5456}{3}n-2756 && (n\ge6),\\ \mathrm{EDD}(\mathcal{R}_n^{3,2})&=\frac{80}{3}n^3-368n^2+\frac{5068}{3}n-2580 && (n\ge6),\\ \mathrm{EDD}(\mathcal{R}_n^{3,1})&=\frac{21}{2}n^3-\frac{317}{2}n^2+793n-312 && (n\ge8). \end{aligned}$$

These formulas are conjectural Euclidean distance degrees for resectioning varieties. The source states that all formulas are new to the authors' knowledge except $\mathrm{EDD}(\mathcal{R}_n^{3,2})$, attributed to an earlier conjecture.