Almost-everywhere polynomial-time computability of Julia sets

Let $f$ be a rational map of degree $d\geqslant 2$, and let $J_f$ denote its Julia set.

Almost-everywhere computability conjecture. For almost all rational maps $f$ of degree $d\geqslant 2$, $J_f$ is polynomial-time computable.

The conjecture is the combined expected consequence of the preceding critical-orbit dichotomy and the conditional computability result. The source gives no resolution, so it remains open.