For self-consistent ion-beam simulations including electron motion, it is desirable to be able to follow electron dynamics accurately without being constrained by the electron cyclotron timescale. To this end, we have developed a particle-advance that interpolates between full particle dynamics and drift motion. By making a proper choice of interpolation parameter, simulation particles experience physically correct parallel dynamics, drift motion, and gyroradius when the timestep is large compared to the cyclotron period, though the effective gyro frequency is artificially low; in the opposite timestep limit, the method approaches a conventional Boris particle push. By combining this scheme with a Poisson solver that includes an interpolated form of the polarization drift in the dielectric response, the movers utility can be extended to higher-density problems where the plasma frequency of the species being advanced exceeds its cyclotron frequency. We describe a series of tests of the mover and its application to simulation of electron clouds in heavy-ion accelerators.