Digital identity and battery-passport systems can make electric-vehicle battery lifecycle records traceable, but traceability alone does not guarantee verifiable evidence or physical recycling compliance. We develop a normative two-stage Stackelberg model in which a regulator chooses audit intensity and verified incentives and a representative obligated firm jointly chooses pre-verification evidence quality and recycling compliance. The benchmark is stress-tested under reduced eligibility-confirmation effectiveness, alternative evidence–recycling interaction, decentralized manufacturer–recycler decisions, and implementation costs. Baseline traceability can leave evidence quality at the reporting floor and compliance incomplete, while additional responsibility exposure can conditionally increase recycling compliance while reducing evidence quality. Coordinated verified incentives improve both decisions and welfare in the benchmark complementarity domain. At zero eligibility-confirmation effectiveness, the fixed positive-rate package can become marginally welfare-inferior under finite capacity; adverse interaction can reverse a cross-effect, decentralization creates coordination underinvestment, and high payment or startup costs create single- or no-positive-payment regions. The model is therefore a forward-looking governance analysis rather than an empirical evaluation or legal calibration of current Chinese or European Union rules.