Large language models (LLMs) show remarkable potential in scientific hypothesis discovery. However, existing approaches face two critical limitations: they treat divergent exploratory search and convergent fine-grained refinement as isolated tasks, and they operate autonomously with little to no human guidance. We present MOOSE-Copilot, the first unified framework to bridge this abstraction gap through a formalized human-AI interaction (HAII) protocol. Our system empowers scientists to steer the generative process via three explicit signals: initial blueprints, inter-stage routing, and intra-stage feedback. Using an oracle-simulated evaluation in which an LLM provides idealized expert signals, we show that injecting these structured signals significantly outperforms purely autonomous baselines, characterizing the gains achievable under high-quality guidance. Furthermore, we build a web-based interface that turns the framework into a no-code workflow: researchers pose a question, watch the hypothesis search unfold as an interactive tree, and steer it by selecting hypotheses, routing between stages, and injecting feedback-no command-line agents required. This makes end-to-end hypothesis discovery directly accessible to interdisciplinary researchers.