Transliterating Vietnamese National Scripts (chữ Quốc Ngữ) (phonetic) into Sino-Nom Scripts (chữ Hán Nôm) (logographic) is challenging: a single syllable may correspond to many characters and disambiguation becomes harder when contextual cues are sparse or absent. Existing SMT-based tools often choose incorrect characters and perform poorly with punctuation or irregular formatting. We propose a T5-based system with two fine-tuned branches: a Vietnamese-Sino model trained on 7 million aligned Vietnamese-Traditional Chinese pairs and a Vietnamese-Nom model trained on 27 thousand Vietnamese-Nom pairs. A decision tree classifier routes inputs to the appropriate branch, while sliding-window decoding improves long-sequence handling. Post-processing with OpenCC normalizes variant forms. On 5,003 mixed Sino-Nom sequences, our system achieves BLEU 69.73 and CER 0.16, outperforming both the baseline T5 (38.74, 0.38) and the CLC tool (38.83, 0.38). These results demonstrate substantial gains in transliteration accuracy and robustness for Vietnamese National Scripts to Sino-Nom Scripts conversion.