In a closed-loop supply chain system consisting of a new energy vehicle manufacturer, a retailer, and a battery manufacturer, three hybrid channel recovery models are proposed: manufacturer and retailer recovery (Model A), manufacturer and battery manufacturer recovery (Model B), and manufacturer, retailer, and battery manufacturer recovery (Model C). Using Stackelberg game theory, the Nash equilibrium solutions for each model are derived, and the selection of hybrid channel recovery models for retired power batteries under government subsidies to the vehicle manufacturer is investigated. The findings indicate that: 1) the manufacturer’s optimal model changes dynamically with increasing subsidies: Model C is chosen when subsidies are low, Model B is preferred when subsidies are moderate or relatively high, and Model A becomes more favorable when subsidies are very high; 2) the retailer’s optimal model depends on a trade-off between recovery competition and channel benefits: Model C is selected when subsidies are low or moderate, Model A is chosen when subsidies are relatively high, yet the retailer achieves the highest profit under Model B—where it does not participate in recovery—when subsidies are extremely high; 3) The battery manufacturer’s model choice is determined by the subsidy level: it earns higher profits under Model B when subsidies are low, but gains greater benefits under Model C when subsidies are relatively high.