Accent normalization (AN) systems often struggle with unnatural outputs and undesired content distortion, stemming from both suboptimal training data and rigid duration modeling. In this paper, we propose a "source-synthesis" methodology for training data construction. By generating source L2 speech and using authentic native speech as the training target, our approach avoids learning from TTS artifacts and, crucially, requires no real L2 data in training. Alongside this data strategy, we introduce CosyAccent, a non-autoregressive model that resolves the trade-off between prosodic naturalness and duration control. CosyAccent implicitly models rhythm for flexibility yet offers explicit control over total output duration. Experiments show that, despite being trained without any real L2 speech, CosyAccent achieves significantly improved content preservation and superior naturalness compared to strong baselines trained on real-world data.