Conjecture on removing assumptions from the uniqueness of Poincaré duality models

Let $V$ be a differential Poincaré duality algebra with \H^0(V)=\operatorname{Span}\{1\} and \H^1(V)=0, and let $\Model_1$ and $\Model_2$ be Poincaré duality models satisfying the hypotheses of Proposition 3.?? except for its additional assumptions. Uniqueness conjecture. The additional assumptions of the proposition can be removed, so $\dIBL^\MC(\CycC(\Model_1))$ and $\dIBL^\MC(\CycC(\Model_2))$ are $\IBLInfty$-quasi-isomorphic. This would make the canonical construction independent of the auxiliary model under the basic hypotheses, but the source gives no resolution.