Hi Mike, thanks for your question. In short, the answer is no. Roemer’s measurement does not prove that the one-way speed of light is constant because it already assumes the standard synchronization (Roemer used Newtonian absolute time).
In the ASC, the synchronization of clocks depends on the distance to the observer. So when the distance from Earth to Jupiter is large, the clocks near Jupiter are set differently than when the distance to Earth is relatively small. The different settings of these clocks correct exactly for the difference in distance. So applying the ASC would give you zero minutes traveling time for both distances, i.e., infinite speed would be measured in both cases (towards the observer on Earth).