The recent demonstration of resonant tunneling transport in nitride semiconductors has led to an invigorated effort to harness this quantum transport regime for practical applications. In polar semiconductors, however, the interplay between fixed polarization charges and mobile free carriers leads to asymmetric transport characteristics. Here, we investigate the possibility of using degenerately doped contact layers to screen the built-in polarization fields and recover symmetric resonant injection. Thanks to a high doping density, negative differential conductance is observed under both bias polarities of GaN/AlN resonant tunneling diodes (RTDs). Moreover, our analytical model reveals a lower bound for the minimum resonant-tunneling voltage achieved via uniform doping, owing to the dopant solubility limit. Charge storage dynamics is also studied by impedance measurements, showing that at close-to-equilibrium conditions, polar RTDs behave effectively as parallel-plate capacitors. These mechanisms are completely reproduced by our analytical model, providing a theoretical framework useful in the design and analysis of polar resonant-tunneling devices.