While Kinetic Monte Carlo (KMC) techniques provide a powerful means to model polymer microstructure, the associated computational cost has been a barrier to their widespread adoption. The case of radical semibatch polymerization under starved-feed policy is a particularly challenging application: at the initial stage, a large simulation volume is required to accurately represent the low concentration of radicals generated at the start of the reaction, while the reactant feed dictates the further increase of the simulation volume with time. A combination of approaches is implemented in a stepwise fashion to greatly accelerate the KMC representation of this system. First, a correction factor is developed to maintain a constant simulation volume in order to improve the efficiency of the solution, followed by scaling of the reaction rates to preserve accuracy at low control volumes and further reduce computational effort. A novel strategy for storing the explicit chain sequences and parallel analysis of the stochastic data is also implemented, with the computational time required to accurately represent a semibatch radical copolymerization test case reduced from 50 to less than 2 min. The accelerated stochastic approach provides a foundation for future optimization of feeding strategies to minimize the fraction of nonfunctionalized chains formed during the production of low molar mass copolymers.