The field of ultra-high-energy cosmic ray (UHECR) astronomy has been facing an ongoing challenge due to the unknown impact of magnetic deflections on the observed events. However, with the dawn of the era of mass-sensitive data, we would have the available information to perform UHECR astronomy. To do so, constructing a sophisticated analysis that can accurately reconstruct source parameters will be crucial. In this work, we construct a Bayesian hierarchical framework that utilises the spatial, energy, and mass composition information to infer the source properties such as luminosity or the spectral index as well as the strength of the extragalactic magnetic field while marginalising the uncertainties of the detector. We model the mass-dependent spatial deflections from the Galactic magnetic field (GMF) on an event-by-event basis using the latest available GMF model (Unger & Farrar 2023, ApJ 970 1, 95) and developed a novel method to determine the nuclear composition of each UHECR source by applying the propagation solver PriNCe (Heinze et al. 2019, ApJ 873 1, 88) that incorporates the energy losses due to photo-nuclear interactions. We apply this new method on realistic simulated datasets with nuclear composition information observed in both Northern and Southern skies to demonstrate the method’s capabilities of the Bayesian inference of source parameters. It is shown that leveraging the full three-dimensional mass-sensitive data while incorporating the most accurate physical models of UHECR acceleration and propagation allows a more unbiased reconstruction of source properties and extragalactic magnetic field strengths.