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Discrete body of revolution (DBOR) codes can accelerate moment method (MoM) solutions for scattering geometries possessing discrete circular symmetry. Traditional DBOR formulations require modifications to the incident field, such as decomposition into circular modes. While appropriate for methods employing direct solvers; approaches employing iterative solvers are disadvantaged by this dramatic increase in the number of right-hand sides that must be solved. In this correspondence, we show how the block circulant property of the impedance matrix can be exploited to avoid incident field modification while compressing matrix storage and accelerating computation of the iterative solver's associated matrix-vector product above that of the typical iterative MoM approach.