Kontsevich's quasi-isomorphism invariance conjecture for polyvector-field cohomology

Let $(A_1,Q_1)$ and $(A_2,Q_2)$ be commutative smooth differential graded algebras that are quasi-isomorphic. Write $T^\bullet_{\mathrm{poly}}(A_i,Q_i)$ for their differential graded algebras of polyvector fields.

Kontsevich's invariance conjecture. There should be an isomorphism of algebras

$$H^\bullet(T^\bullet_{\mathrm{poly}}(A_1,Q_1))\simeq H^\bullet(T^\bullet_{\mathrm{poly}}(A_2,Q_2)).$$

This is needed to make the polyvector-field side of the Duflo formula independent of the chosen quasi-isomorphic model; the source presents it as a conjectural invariance statement.