Alon–Tarsi bound for combined vertex-edge-face graphs

Let $G$ be a plane graph, and let $\overline{G}_{vef}$ denote its combined vertex-edge-face graph. The Alon–Tarsi conjecture. Every plane graph $G$ satisfies

$$\operatorname{AT}(\overline{G}_{vef})\leqslant 7.$$

If true, this would improve the preceding Alon–Tarsi bound for $\overline{G}_{vef}$ and the known list-colouring bound $\operatorname{ch}(\overline{G}_{vef})\leqslant 8$; the source notes that the latter bound's tightness is unknown.