steady-state Galaxy?

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 torus programme. However, this program and all the others (going back to Schwarzschild) make the assumption that the potential is time-independent and has no orbiting substructure (a kind of time-dependence). Binney and others suggest that the time-dependence could be seen in residuals of any fit, but that is not clear to me, and it is also not clear that such a discovery of time dependence would permit good analysis of the time dependence.

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.