The emergence of AI-powered Large Language Models (LLMs), such as ChatGPT and Google Gemini, presents both opportunities and challenges for higher education, particularly regarding academic integrity in writing instruction. This exploratory study examines a novel pedagogical approach that integrates LLMs as required feedback tools in a university-level psychology writing assignment. The exclusive online approach emphasizes improvement through revision, requiring students to obtain AI-generated feedback on ungraded initial drafts based on an instructor-provided rubric, with final assessment focused on the quality of subsequent revisions. Analysis of survey data from 39 undergraduate students, incorporating both quantitative measures and qualitative responses, revealed several key findings. Students consistently reported high utility of LLM feedback, particularly valuing its specificity and actionable guidance. The structured integration of AI feedback appeared to foster learner independence while addressing ethical concerns, with students clearly distinguishing between using AI for feedback versus content generation. Moreover, the assignment's emphasis on iterative improvement over initial performance was perceived to reduce academic integrity pressures. These preliminary findings suggest that thoughtfully structured LLM integration can enhance the writing process while maintaining academic rigor, offering promising directions for pedagogical innovation in technology-enhanced learning environments. Implications for writing instruction and future research in higher education are discussed.