Conjecture on Cartan- and Melikyan-type maximal subalgebras in E_8

Let $G$ be an algebraic group of type $E_8$ with Lie algebra $\mathfrak{g}=\operatorname{Lie}(G)$ over a field of characteristic $5$. Let $M$ be a maximal subalgebra of Cartan or Melikyan type in $\mathfrak{g}$. The Cartan–Melikyan classification conjecture. Then

$$M\cong W(1;2)_{[5]}.$$

The surrounding results establish uniqueness of the conjugacy class of $W(1;2)$ subalgebras and maximality of its $p$-closure, but the stated classification is presented as a conjecture.