Generic ED and GD degree formulas for surfaces and threefolds in ${\rm Gr}(2,4)$

Let a surface in ${\rm Gr}(2,4)$ be defined by generic polynomials of degrees $d_1,d_2$, and let a threefold in ${\rm Gr}(2,4)$ be defined by a generic polynomial $f$ of degree $d$. The ED degree and GD degree refer respectively to the Euclidean-distance and Grassmannian-distance optimization problems. Generic degree conjecture. The GD degree of the surface is

$$2d_1d_2(d_1^2+d_2^2+d_1d_2+2),$$

which is $2d_1d_2$ less than its ED degree. The threefold has ED degree $2d(d^3+3d+2)$ and GD degree $2d(d^3+2d)$. These formulas are stated as conjectural in the supplied span, while nearby results prove related ED-degree formulas.