Gorenstein cohomology conjecture for three-variable cochain DG skew polynomial algebras

Let $k$ be the base field, let $M\in M_3(k)$, and let $\mathcal{A}_{\mathcal{O}_{-1}(k^3)}(M)$ denote the associated cochain DG skew polynomial algebra. Write $H(\mathcal{A}_{\mathcal{O}_{-1}(k^3)}(M))$ for its cohomology algebra. Gorenstein cohomology conjecture. For any $M\in M_3(k)$, $H(\mathcal{A}_{\mathcal{O}_{-1}(k^3)}(M))$ is a left (right) Gorenstein graded algebra. The analogous assertion is known for the corresponding two-variable algebras, where the cohomology is always AS-Gorenstein; this conjecture proposes the corresponding Gorenstein property in three variables.