With the emergence of new topics on social media as sources of rumor dissemination, addressing the distribution shifts between source and target domains remains a crucial task in cross-domain rumor detection. Existing feature alignment methods, which aim to reduce the discrepancies between domains, are often susceptible to task interference during training. Additionally, data distribution alignment methods, which rely on existing data to synthesize new training samples, inherently introduce noise. To deal with these challenges, a new cross-domain rumor detection method, MONTROSE, is proposed. It combines LLM-driven Monte Carlo Tree Search (MCTS) data synthesis to generate high-quality synthetic data for the target domain and a domain-sharpness-aware (DSAM) self-refinement approach to train rumor detection models with these synthetic data effectively. Experiments demonstrate the superior performance of MONTROSE in cross-domain rumor detection.