Health-related speech datasets are often small and varied in focus. This makes it difficult to leverage them to effectively support healthcare goals. Robust transfer of linguistic features across different datasets orbiting the same goal carries potential to address this concern. To test this hypothesis, we experiment with domain adaptation (DA) techniques on heterogeneous spoken language data to evaluate generalizability across diverse datasets for a common task: dementia detection. We find that adapted models exhibit better performance across conversational and task-oriented datasets. The feature-augmented DA method achieves a 22\% increase in accuracy adapting from a conversational to task-specific dataset compared to a jointly trained baseline. This suggests promising capacity of these techniques to allow for productive use of disparate data for a complex spoken language healthcare task.