Free-action conjecture for quantization of quasi-Poisson manifolds

Let $({\mathfrak{g}},Z)$ consist of a finite-dimensional Lie algebra ${\mathfrak{g}}$ and an invariant element $Z$, and let $X$ be a quasi-Poisson manifold for $({\mathfrak{g}},Z)$. Let $G$ be the simply connected Lie group corresponding to ${\mathfrak{g}}$. The ${\mathfrak{g}}$-action on $X$ is free when $X$ is a principal $G$-bundle over the quotient $Y=X/G$.

Free-action quantization conjecture. A quasi-Poisson manifold $X$ for $({\mathfrak{g}},Z)$ can be quantized if the ${\mathfrak{g}}$-action on $X$ is free, i.e. if $X$ is a principal $G$-bundle over $Y=X/G$, where $G$ is the simply connected Lie group corresponding to ${\mathfrak{g}}$.

The conjecture proposes a sufficient condition for quantizability after the paper explains that arbitrary quasi-Poisson manifolds need not be quantizable, even in symplectic cases. The supplied text gives no resolution, so the conjecture remains open.