Freudenburg's conjugacy conjecture for maximal Lie subalgebras

Let $\mathbb{K}$ be a field of characteristic zero, let $\mathbb{K}[x_1,\ldots,x_n]$ be the polynomial algebra in $n$ variables, and let $\operatorname{LND}(\mathbb{K}[x_1,\ldots,x_n])$ denote its locally nilpotent derivations. Define

$$\mathfrak{T}=\mathbb{K}\partial_{x_1}\oplus\cdots\oplus\mathbb{K}[x_1,\ldots,x_{n-1}]\partial_{x_n}.$$

Freudenburg's conjugacy conjecture. Every maximal Lie subalgebra $\mathcal{A}\subset\operatorname{LND}(\mathbb{K}[x_1,\ldots,x_n])$ is conjugate to $\mathfrak{T}$. This is the uniqueness-up-to-conjugation part of Freudenburg's proposed structure theory for maximal Lie subalgebras of locally nilpotent derivations; the supplied text gives no evidence of resolution.