Abstract: Rhombohedral stacked graphene (RSG) contains two key ingredients for the realization of correlated topological phases of matter: flat electronic bands and concentrated Berry curvature. The fractional quantum anomalous Hall effect was recently observed in an RSG-hexagonal boron nitride (hBN) moiré heterostructure when the conduction electrons were pushed away from the moiré interface by an applied electric displacement field. The question then arises about whether such topological states can also develop in RSG-hBN in a strong moiré potential. Here, we explore the physics in the moiré-proximal limit through capacitance measurements that allow us to determine the electronic compressibility and extract energy gaps of incompressible states. We report the observation of low-field integer and fractional Chern insulator states in this limit at filling factors v = 1, 2/3, and 1/3 in addition to numerous trivial and topological charge density waves. We map out a correlated phase diagram that is highly sensitive to both displacement and magnetic fields, establishing the moiré-proximal regime as a tunable platform for studying the interplay between band topology and strong lattice effects.