Recent neural audio codec-based speech generation (CodecFake) produces highly realistic audio, posing a challenge to existing deepfake countermeasure models. While using codec resynthesized speech (CoRS) as proxy data improves performance, it often suffers from limited generalization. We propose Domain-Shift Feature Augmentation (DSFA), which simulates "in-the-wild" variations by transforming deterministic feature statistics into stochastic distributions during fine-tuning. To evaluate generalization, we further introduce Codec-based Speech Generation Extension Evaluation (CoSG ExtEval) dataset, a more challenging extension of the CoSG Eval (from CodecFake+) dataset, featuring 40 unseen generative models and long-form audio. Experimental results demonstrate that combining a post-trained SSL backbone with DSFA effectively narrows the proxy-to-wild domain gap. This approach achieves state-of-the-art performance across diverse CodecFake attacks in both CoSG Eval and CoSG ExtEval.