Unified streaming and offline ASR aims to deliver full-context accuracy and low-latency incremental decoding with a single model. Transformer/Conformer systems are effective, but long-form streaming inference still suffers from growing attention masks, historical caches, and memory states. Latency-Controlled BiMamba (LC-BiMamba) offers attention-free bidirectional modeling, yet its backward branch is confined to fixed chunks, tying the model to one latency. Extending it to dynamic chunk training expands mini-batches and slows training. We propose TC-BiMamba, whose Trans-Chunk formulation casts local-future backward modeling as sequence-level dynamic-chunk training over complete sequences. TC-BiMamba supports multiple chunk-wise latency settings, keeps the encoder/CTC path memory-stable on long-form inputs, and improves training scalability. On AISHELL-1, AISHELL-2, and LibriSpeech, it outperforms U2++ and remains competitive with externally reported LC-BiMamba results using fewer parameters, while achieving 1.3 times training speedup and 50% GPU memory reduction.