Modern serving systems for Mixture-of-Experts (MoE) models adopt hybrid data-expert parallelism: expert parallelism (EP) shards experts across GPUs to scale capacity, while data parallelism (DP) replicates attention layers across instances to process independent requests. Existing systems bind each request's attention, MoE communication, and KV cache to a single instance. Because attention latency scales with KV cache size while MoE communication latency scales with batch size, this binding cannot balance both simultaneously, producing EP stragglers; it also fragments KV memory across instances, inflating tail latency under long contexts. While existing context parallelism (CP) mitigates these constraints, its uniform parallelism degree incurs prohibitive communication and attention-side overheads. We present \work, which decouples MoE communication from KV cache placement and achieves dual balance through dynamic context parallelism (DCP). DCP assigns each request a context-parallel degree sized to its KV footprint: long requests distribute attention across multiple instances; short requests remain local. This dynamic parallelism effectively liquefies the KV cache across the cluster, balancing both the per-instance KV cache occupancy and batch sizes without unnecessary load-balancing costs. To bridge DCP with static execution, \work introduces an ahead-of-time (AOT) graph engine paired with a custom routing-based communication backend. Experimental results show that \work maintains up to $1.88\times$--$3.27\times$ higher request rates under strict time-per-output-token (TPOT) service level objectives (SLOs). Furthermore, \work significantly mitigates stragglers, reducing P99 tail latency by up to $1.79\times$--$2.12\times$.

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