We examine the density dependence of the hydrodynamic response of superfluid helium to classical rotational motion of a molecular impurity within the assumption of an adiabatically following helium density. The sensitivity of the hydrodynamic response to small changes in the helium density is assessed by performing three-dimensional hydrodynamic calculations for different fits to a microscopic helium density around the octahedral SF6 molecule generated by finite-temperature path integral Monte Carlo simulations. The sensitivity to systematic errors in the helium solvation density is assessed by comparing the hydrodynamic results obtained with finite-temperature path integral Monte Carlo densities to the corresponding results obtained using zero-temperature diffusion Monte Carlo densities that possess trial function bias. Our analysis shows that the finite-temperature densities provide a robust upper bound on the hydrodynamic response that amounts to at most 10% of the experimentally measured moment of inertia increment for SF6 at low temperature. We also address theoretical consistency requirements on the numerically derived velocity flows and present modifications of the hydrodynamic equations that are required by incorporation of higher-order quantum phase correlations.