We propose a mechanism to substantially rectify radiative heat flow by matching thin films of metal-to-insulator transition materials and polar dielectrics in the electromagnetic near field. By leveraging the distinct scaling behaviors of the local density of states with film thickness for metals and insulators, we theoretically achieve rectification ratios over 140-a 10-fold improvement over the state of the art-with nanofilms of vanadium dioxide and cubic boron nitride in the parallel-plane geometry at experimentally feasible gap sizes (~100 nm). Our rational design offers relative ease of fabrication, flexible choice of materials, and robustness against deviations from optimal film thicknesses. We expect this work to facilitate the application of thermal diodes in solid-state thermal circuits and energy conversion devices.