Quantum machine learning (QML) promises compact and expressive representations, but suffers from the measurement bottleneck - a narrow quantum-to-classical readout that limits performance and amplifies privacy risk. We propose a lightweight residual hybrid architecture that concatenates quantum features with raw inputs before classification, bypassing the bottleneck without increasing quantum complexity. Experiments show our model outperforms pure quantum and prior hybrid models in both centralized and federated settings. It achieves up to +55% accuracy improvement over quantum baselines, while retaining low communication cost and enhanced privacy robustness. Ablation studies confirm the effectiveness of the residual connection at the quantum-classical interface. Our method offers a practical, near-term pathway for integrating quantum models into privacy-sensitive, resource-constrained settings like federated edge learning.