The converse flow conjecture for minimal P-zippers

Let $M$ be a hyperbolic 3-manifold. A minimal P-zipper is a minimal P-zipper $Z^\pm$ for $M$, with endpoint maps denoted $e^\pm$ and corresponding spaces $P^\pm$. The converse flow conjecture. There is a quasigeodesic pseudo-Anosov flow $X$ on $M$ whose endpoint maps satisfy

$$e^\pm(P^\pm)=Z^\pm.$$

Moreover, $X$ has no perfect fits if and only if $Z^\pm$ is a zipper. This would provide a converse to the construction of zippers from quasigeodesic pseudo-Anosov flows, connecting minimal P-zippers with dynamical structures on hyperbolic 3-manifolds.