We explore the use of self-training and acceptability classifiers with pre-trained models for natural language generation in structure-to-text settings using three GEM datasets (E2E, WebNLG-en, Schema-Guided Dialog). With the Schema-Guided Dialog dataset, we also experiment with including multiple turns of context in the input. We find that self-training with reconstruction matching along with acceptability classifier filtering can improve semantic correctness, though gains are limited in the full-data setting. With context-conditioning, we find that including multiple turns in the context encourages the model to align with the user's word and phrasing choices as well as to generate more self-consistent responses. In future versions of the GEM challenge, we encourage the inclusion of few-shot tracks to encourage research on data efficiency.