I spent a chunk of the weekend and this morning working through the literature on modeling the Galaxy as a steady-state system, using phase-space data from Gaia or the projects that precede it. This didn't take long, because there isn't much written on the subject. Several good papers are by Binney, who has a
Interestingly, tidal streams (disrupting satellites and clusters) both measure the potential directly (in some sense, because the streams highlight an orbit or a small family of similar orbits), and show that the Milky Way is not in steady state. I would love to discover the analysis program that makes use of the near-steadiness and the substructure that is not steady to infer the potential and its time dependence all at once.