Charge transport in solid-state materials is often governed by charge carrier hopping processes in the presence of long-range electrostatic interactions. Kinetic Monte Carlo (kMC) simulations provide a framework for describing such rare-event dynamics over extended timescales. However, the efficient treatment of long-range interactions remains a major computational challenge, since each particle jump modifies the energy landscape globally and, in principle, requires updating all transition rates after every carrier motion. We present an efficient and generally applicable update process for these transition rates in the presence of long-range electrostatic interactions. To illustrate the method, we study charge diffusion on a simple cubic host lattice under an external electric field. The transport behavior is investigated in high states of charge (SOC), and the influence of temperature, electric field strength, and SOC is examined. Our simulations show strongly suppressed transport at 100 % SOC (50 % occupation) caused by a freezing of the charge carriers into a Coulomb superlattice. Slight deviations from this reference in terms of charge carrier concentration lead to a rapid increase in conductivity. A deeper analysis reveals that this behavior can be rationalized as transport of non-interacting defects in the Coulomb superlattice. These results demonstrate the capability of the proposed update procedure to efficiently capture non-equilibrium transport phenomena in interacting charged systems and provide a foundation for simulations of more complex charge diffusion problems.