This paper first introduces a computationally efficient approach for conducting a time-series impact analysis of electric vehicle (EV) charging on the loading levels of power system equipment. This study incorporates the stochastic nature of EV owners' charging behaviours by modelling various charging profiles as probability distributions. This work then develops new mitigation strategies to temporally shift EV charging from periods of equipment overloading to alternative time periods to improve power system equipment lifetime. A reward program and a time-of-use (TOU) tariff are proposed to incentivize EV owners to participate to the mitigation effort. A search algorithm integrating a convex optimization problem is developed to determine optimal incentive levels and quantify resulting changes in EV owner charging behaviours. The proposed mitigation strategies are numerically evaluated on a modified version of the large-scale IEEE-8500 test feeder with a high EV penetration to mitigate the overloading of the substation transformer.