Conversational Tree Search (V\"ath et al., 2023) is a recent approach to controllable dialog systems, where domain experts shape the behavior of a Reinforcement Learning agent through a dialog tree. The agent learns to efficiently navigate this tree, while adapting to information needs, e.g., domain familiarity, of different users. However, the need for additional training data hinders deployment in new domains. To address this, we explore approaches to generate this data directly from dialog trees. We improve the original approach, and show that agents trained on synthetic data can achieve comparable dialog success to models trained on human data, both when using a commercial Large Language Model for generation, or when using a smaller open-source model, running on a single GPU. We further demonstrate the scalability of our approach by collecting and testing on two new datasets: ONBOARD, a new domain helping foreign residents moving to a new city, and the medical domain DIAGNOSE, a subset of Wikipedia articles related to scalp and head symptoms. Finally, we perform human testing, where no statistically significant differences were found in either objective or subjective measures between models trained on human and generated data.