The schema-guided paradigm overcomes scalability issues inherent in building task-oriented dialogue (TOD) agents with static ontologies. Rather than operating on dialogue context alone, agents have access to hierarchical schemas containing task-relevant natural language descriptions. Fine-tuned language models excel at schema-guided dialogue state tracking (DST) but are sensitive to the writing style of the schemas. We explore methods for improving the robustness of DST models. We propose a framework for generating synthetic schemas which uses tree-based ranking to jointly optimise lexical diversity and semantic faithfulness. The robust generalisation of strong baselines is improved when augmenting their training data with prompts generated by our framework, as demonstrated by marked improvements in average Joint Goal Accuracy (JGA) and schema sensitivity (SS) on the SGD-X benchmark.