In this work, we perform a self-consistent numerical analysis of a cyclotron resonance maser accelerator operating with arbitrary amplitudes of the maser beam. We basically investigate the interplay involving wave dispersion, a possible mismatch between cyclotron and wave frequencies, and the initial gyrophase spread of the distribution function for the accelerating particles. It is shown that for small enough initial values of particle energies, rapid phase bunching takes place. In this case, we show how a convenient choice of the mismatch parameter can greatly reduce the limiting influence of wave dispersion on particle bulk acceleration. On the other hand, when initial energies are larger, it is shown that phase bunching does not occur and that a considerable energy spread may set in. Even in this case, however, a convenient choice of the mismatch parameter can still cause energization for a fraction of the injected particles, although beam quality is reduced. A comparison between numerical simulation and the self-consistent macroparticle analysis is also carried out.