Closure of strong Keller maps under composition

Let $k$ be a field of characteristic $p$. A strong Keller map is a polynomial endomorphism in $\operatorname{SKE}_n(k)$ satisfying the universal Keller equations. Composition conjecture. The set $\operatorname{SKE}_n(k)$ is closed under composition:

$$f,g\in \operatorname{SKE}_n(k)\quad\Longrightarrow\quad f\circ g\in \operatorname{SKE}_n(k).$$

The paper proves a bounded-degree, bounded-coefficient version for sufficiently large $p$, but leaves the unrestricted characteristic-$p$ statement as the generic case that remains unresolved.