Reduction of La1-xCaxMnO3 (0.6 <= x <= 1) perovskite phases with sodium hydride yields materials of composition La1-xCaxMnO2+delta. The calcium-rich phases (x = 0.9, 1) adopt (La0.9Ca0.1)(0.5)Mn0.5O disordered rocksalt structures. However local structure analysis using reverse Monte Carlo refinement of models against pair distribution functions obtained from neutron total scattering data reveals lanthanum-rich La1-xCaxMnO2+delta (x = 0.6, 0.67, 0.7) phases adopt disordered structures consisting of an intergrowth of sheets of MnO6 octahedra and sheets of MnO4 tetrahedra. X-ray absorption data confirm the presence of Mn(I) centers in La1-xCaxMnO2+delta phases with x < 1. Low-temperature neutron diffraction data reveal La1-xCaxMnO2+delta (x = 0.6, 0.67, 0.7) phases become antiferromagnetically ordered at low temperature.