Carrier phase positioning (CPP) can enable cm-level accuracy in next-generation wireless systems, while recent literature shows that accuracy remains high using phase-only measurements in distributed MIMO (D-MIMO). However, the impact of phase synchronization errors on such systems remains insufficiently explored. To address this gap, we first show that the proposed hyperbola intersection method achieves highly accurate positioning even in the presence of phase synchronization errors, when trained on appropriate data reflecting such impairments. We then introduce a deep learning (DL)-based D-MIMO antenna point (AP) selection framework that ensures high-precision localization under phase synchronization errors. Simulation results show that the proposed framework improves positioning accuracy compared to prior-art methods, while reducing inference complexity by approximately 19.7%.