We present a generalized Ramo-Shockley theorem (GRST) for the calculation of time-dependent terminal currents in multidimensional charge transport calculations and simulations. While analytically equivalent to existing boundary integration methods, this new domain integration technique is less sensitive to numerical error introduced by calculations of finite precision. Most significantly, we derive entirely new optimized formulas for the ensemble Monte Carlo estimation of steady-state terminal currents from the time-independent form of our GRST, which are in general not equivalent to the time-average of the true time-dependent terminal currents. We then demonstrate, both analytically and by means of example, how our new variance-minimizing terminal current estimators may be exploited to improve estimator accuracy in comparison to existing methods.