Spatial variations of the average properties that characterize the hadronic component of the diffuse Galactic cosmic-ray sea, in particular the spectral slope and normalization, may unveil critical information about their confinement mechanism in the Galaxy. In the first part of this paper we perform an analysis of the Fermi-LAT gamma-ray data with the SkyFACT package, which combines image reconstruction techniques with standard template fitting, isolate the hadronic emission and decompose it into Galactocentric rings. We find a significant hardening of the hadronic spectral index towards the molecular ring. We study this hardening in different energy ranges, and assess its resilience with respect to different prescriptions in the analysis setup. In the second part we quantify the contribution to the diffuse gamma-ray flux coming from unresolved point sources with a dedicated Monte Carlo simulation, and consider whether the trend characterized in the first part can be mimicked by a progressively more relevant flux associated to this component in the inner Galaxy. We find that the observed hardening of the hadronic spectral index cannot be due to unresolved sources in the sub-TeV energy range, especially outside the molecular ring, given reasonable assumptions about the unresolved source population.