Maubach–Poloni's GLIN conjecture for polynomial automorphism groups

Let $\mathbb{K}$ be a field, and let ${\rm GA}_n(\mathbb{K})$ denote the group of polynomial automorphisms of affine $n$-space over $\mathbb{K}$. Let ${\rm GLIN}_n(\mathbb{K})$ be the subgroup introduced by Maubach and Poloni consisting of automorphisms satisfying their linearization property. Maubach–Poloni's conjecture. If $\mathbb{K}\neq\mathbb{F}_2$, then

$${\rm GLIN}_n(\mathbb{K})={\rm GA}_n(\mathbb{K}).$$

This is trivial for $n=1$ and follows from the Jung–van der Kulk theorem for $n=2$, but remains open for $n\geq 3$. The hypothesis $\mathbb{K}\neq\mathbb{F}_2$ is necessary.