Conjecture on radical maximal subalgebras of type E_8 in characteristic five

Let $G$ be an algebraic group of type $E_8$ with Lie algebra $\mathfrak{g}=\operatorname{Lie}(G)$ over an algebraically closed field of characteristic $5$. Let $M$ be a maximal subalgebra with nonzero radical, and let $\mathfrak{w}$ denote the maximal subalgebra defined in Theorem 4.3. The classification conjecture. Every such $M$ is either conjugate to $\mathfrak{w}$ under the adjoint action of $G$, is the Lie algebra of a maximal parabolic subgroup $P$ of $G$, or is the centraliser of a toral element $t\in\mathfrak{g}$. In the last case, $M=\operatorname{Lie}(G_t)$ and $G_t$ is semisimple of type $A_4A_4$. This proposes a complete description of maximal subalgebras with nonzero radical in this case; the statement is presented as a conjecture, with no resolution supplied in the source.