Neural linguistic steganography aims to embed information into natural text while preserving statistical undetectability. A fundamental challenge in this ffeld stems from tokenization ambiguity in modern tokenizers, which can lead to catastrophic decoding failures. The recent method, SyncPool, addresses this ambiguity by employing a coarse-grained synchronization mechanism over groups of ambiguous candidates. However, SyncPool sacriffces embedding capacity, as it utilizes the entire Shannon entropy of an ambiguous group solely for synchronization rather than for payload embedding. We propose a method named look-ahead Sync, which overcomes the capacity limitation of SyncPool while retaining its provable security guarantees. Our approach performs minimal synchronized sampling only on truly indistinguishable token sequences, while strategically preserving all other discernible paths to maximize embedding capacity. We provide theoretical proofs for the security of our method and analyze the gap between its achievable embedding capacity and the theoretical upper bound. Experiments on English (using Llama 3) and Chinese (using Qwen 2.5) benchmarks show that our method consistently approaches the theoretical capacity upper bound and signiffcantly outperforms SyncPool. The improvement in embedding rate exceeds 160% in English and 25% in Chinese, particularly in settings with larger candidate pools. This work represents a signiffcant step toward practical high-capacity provably secure linguistic steganography.