Black hole accretion flows show rapid X-ray variability. The power spectral density (PSD) of this is typically fit by a phenomenological model of multiple Lorentzians for both the broad-band noise and quasi-periodic oscillations (QPOs). Our previous paper developed the first physical model for the PSD and fit this to observational data. This was based on the same truncated disc/hot inner flow geometry which can explain the correlated properties of the energy spectra. This assumes that the broad-band noise is from propagating fluctuations in mass accretion rate within the hot flow, while the QPO is produced by global Lense–Thirring precession of the same hot flow. Here we develop this model, making some significant improvements. First, we specify that the viscous frequency (equivalently, surface density) in the hot flow has the same form as that measured from numerical simulations of precessing, tilted accretion flows. Secondly, we refine the statistical techniques which we use to fit the model to the data. We re-analyse the PSD from the 1998 rise to outburst of XTE J1550−564 with our new model in order to assess the impact of these changes. We find that the derived outer radii of the hot flow (set by the inner radius of the truncated disc) are rather similar, changing from ∼68 to 13Rg throughout the outburst rise. However, the more physical assumptions of our new model also allow us to constrain the scaleheight of the flow. This decreases as the outer radius of the flow decreases, as expected from the spectral evolution. The spectrum steepens in response to the increased cooling as the truncation radius sweeps in, so gas pressure support for the flow decreases. The new model, propfluc, is publicly available within the xspec spectral fitting package.