By employing the Massieu formalism presented in the preceding paper, Monte Carlo methods and extrapolation techniques are combined to simulate polymers with chain-length polydispersity. Semigrand canonical and grand canonical ensembles supplemented by identity exchange moves and expanded-ensemble moves have been tailored to simulate both thermodynamic properties and the structure of various coarse-grained model systems. It is demonstrated that the proposed methods can be used to simulate systems with arbitrary molecular weight distribution (e.g., to match experimental data), bulk-pore partitioning of polymer solutions, and liquid-liquid equilibrium of polydisperse polymer melts.