To improve the prediction accuracy of $\alpha$-decay half-lives in heavy and superheavy nuclei, a physics-guided residual-correction framework combining the effective liquid drop model (ELDM) with machine-learning methods is proposed. The ELDM is first used as the macroscopic baseline for describing the barrier-penetration process, and XGBoost and TabPFN models are then employed to learn the residual deviations between ELDM predictions and experimental data. Several physically motivated descriptors associated with nuclear deformation, Coulomb–decay-energy systematics, and minimum orbital angular momentum are introduced into the residual-learning process. In the global 10-fold cross-validation comparison, TabPFN-term3 achieves the lowest prediction errors, reducing the RMSE and MAE from 0.567 and 0.417 for the ELDM baseline to 0.348 and 0.248, corresponding to improvements of 38.62% and 40.53%, respectively. Regional, parity-separated, and superheavy extrapolation analyses further support the effectiveness and transferability of the residual-correction framework. Overall, the proposed approach effectively reduces systematic deviations not fully described by the macroscopic ELDM baseline while retaining a direct connection to the underlying $\alpha$-decay physics.