Exceptional Dynkin zigzag intrinsic formality conjecture

Let $\mathbb{K}$ be a ground field of characteristic zero, let $\Gamma$ be a tree of type $E_6$, $E_7$, or $E_8$, and let $A_\Gamma$ be the corresponding zigzag algebra. Exceptional Dynkin intrinsic formality conjecture. The zigzag algebra $A_\Gamma$ is intrinsically formal: every $A_\infty$-algebra whose cohomology is isomorphic to $A_\Gamma$ is quasi-isomorphic to $A_\Gamma$. Intrinsic formality is known in the paper for the $A_n$ and $D_n$ cases under the stated results, while the conjecture concerns the remaining exceptional Dynkin types.