In this paper we expand our previous study on phonon thermal rectification (TR) exhibited in a hybrid graphene-carbon nitride system (G-C3N) to investigate the system's behavior under a wider range of temperature differences, between the two employed baths, and the effects of media-interface geometry on the rectification factor. Our simulation results reveal a sigmoid relation between TR and temperature difference, with a sample-size depending upper asymptote occurring at generally large temperature differences. The achieved TR values are significant and go up to around 120% for ΔT = 150 K. Furthermore, the consideration of varying media-interface geometries yields a non-negligible effect on TR and highlights areas for further investigation. Finally, calculations of Kapitza resistance at the G-C3N interface are performed for assisting us in the understanding of interface-geometry effects on TR.