This paper explores methods for extracting information from radiology reports that generalize across exam modalities to reduce requirements for annotated data. We demonstrate that multi-pass T5-based text-to-text generative models exhibit better generalization across exam modalities compared to approaches that employ BERT-based task-specific classification layers. We then develop methods that reduce the inference cost of the model, making large-scale corpus processing more feasible for clinical applications. Specifically, we introduce a generative technique that decomposes complex tasks into smaller subtask blocks, which improves a single-pass model when combined with multitask training. In addition, we leverage target-domain contexts during inference to enhance domain adaptation, enabling use of smaller models. Analyses offer insights into the benefits of different cost reduction strategies.