Device-cloud speculative decoding reduces server computation, but growing a deep draft tree with a small language model (SLM) requires repeated passes on a mobile neural processing unit (NPU). We present HyCo, which runs the server model's native multi-token prediction (MTP) head on the device to build a deep chain and uses one SLM pass to add alternative branches. The server returns the hidden state, input embedding, and key-value entries needed by the head instead of executing its sequential steps. Quantization, a restricted vocabulary, and a 1K-token window fit both drafters to the NPU. An ε-threshold rule additionally relaxes exact preservation of the verifier's sampling distribution. In single-client runs with a Galaxy S26 Ultra over LTE/5G, HyCo reduces server GPU time per output token relative to server-side MTP self-speculation by 38.6% on Spec-Bench and 29.2% on 32K-token summarization. With the same acceptance rule, three runs of each system on Spec-Bench show 9.0 percentage points more saving and 1.9x delivery speed than an SLM-only drafter. HyCo differs from Cloud+MTP by +0.2 judge-score points (paired 95% CI: -0.9 to +1.3); exploratory translation favors SpecEdge-ε. Without relaxation, HyCo exact saves 27.7% and 11.9% on the two datasets.

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