Passive acoustic monitoring (PAM) for bird classification suffers from a severe domain shift between focal training data and passive deployment environments, a challenge exacerbated by the prohibitive cost of annotating target data. Extensive benchmarking has shown that standard architectures and data augmentations struggle to generalize across this focal-to-passive gap. We propose SNR-Guided Multi-Signal Mix (SG-MSM), a multi-stage data augmentation pipeline that explicitly mitigates the focal-to-passive domain shift. We evaluate SG-MSM across six diverse PAM environments using an EfficientNet-B3, achieving a mean ROC-AUC of 0.884. This outperforms the comprehensive augmentation pipeline established by the BirdSet benchmark and the Perch 1.0 foundation model (860K recordings) across all domains, despite training on orders of magnitude less data (3.6K--28K samples). SG-MSM proves highly competitive with the state-of-the-art Perch 2.0 and BirdMAE models. Component-wise ablation studies isolate the impact of each synthesis stage, demonstrating relative gains of +20.4% in ROC-AUC, +81.4% in cmAP, and +89.5% in Top-1 Accuracy over focal-only training.