This paper addresses the persistent challenge of accurately digitizing paper-based electrocardiogram (ECG) recordings, with a particular focus on robustly handling single leads compromised by signal overlaps-a common yet under-addressed issue in existing methodologies. We propose a two-stage pipeline designed to overcome this limitation. The first stage employs a U-Net based segmentation network, trained on a dataset enriched with overlapping signals and fortified with custom data augmentations, to accurately isolate the primary ECG trace. The subsequent stage converts this refined binary mask into a time-series signal using established digitization techniques, enhanced by an adaptive grid detection module for improved versatility across different ECG formats and scales. Our experimental results demonstrate the efficacy of our approach. The U-Net architecture achieves an IoU of 0.87 for the fine-grained segmentation task. Crucially, our proposed digitization method yields superior performance compared to a well-established baseline technique across both non-overlapping and challenging overlapping ECG samples. For non-overlapping signals, our method achieved a Mean Squared Error (MSE) of 0.0010 and a Pearson Correlation Coefficient (rho) of 0.9644, compared to 0.0015 and 0.9366, respectively, for the baseline. On samples with signal overlap, our method achieved an MSE of 0.0029 and a rho of 0.9641, significantly improving upon the baseline's 0.0178 and 0.8676. This work demonstrates an effective strategy to significantly enhance digitization accuracy, especially in the presence of signal overlaps, thereby laying a strong foundation for the reliable conversion of analog ECG records into analyzable digital data for contemporary research and clinical applications. The implementation is publicly available at this GitHub repository: https://github.com/masoudrahimi39/ECG-code.