A Galactic cosmic-ray transport model featuring non-homogeneous transport has been developed over the latest years. This setup is aimed at reproducing γ-ray observations in different regions of the Galaxy (with particular focus on the progressive hardening of the hadronic spectrum in the inner Galaxy) and was shown to be compatible with the very-high-energy γ-ray diffuse emission recently detected up to PeV energies. In this work, we extend the results previously presented to test the reliability of that model throughout the whole sky. To this aim, we compare our predictions with detailed longitude and latitude profiles of the diffuse γ-ray emission measured by Fermi-LAT for different energies and compute the expected Galactic ν diffuse emission, comparing it with current limits from the ANTARES collaboration. We emphasize that the possible detection of a Galactic ν component will allow us to break the degeneracy between our model and other scenarios featuring prominent contributions from unresolved sources and TeV halos.