Universal quantization conjecture for Lie-quasi bialgebroids

Let a Lie-quasi bialgebroid be a quasi-bialgebroid generalising Lie bialgebroids and quasi-bialgebras, and let a quasi-quantum groupoid be a topological deformation of the standard bialgebroid $\mathcal{U}_{R}(E)$ as a quasi-bialgebroid. Fix a Drinfel'd associator. Yes-go conjecture. Given a Drinfel'd associator, one can define a universal quantization of Lie-quasi bialgebroids as quasi-quantum groupoids. The conjecture is presented as the expected outcome of a formality construction for Lie-quasi bialgebroids; the required $\mathsf{Lie}_\infty$-isomorphism depends on the chosen Drinfel'd associator, and no proof is given in the source.