The ubiquity of technologies like ChatGPT has raised concerns about their impact on student writing, particularly regarding reduced learner agency and superficial engagement with content. While standalone chat-based LLMs often produce suboptimal writing outcomes, evidence suggests that purposefully designed AI writing support tools can enhance the writing process. This paper investigates how different AI support approaches affect writers' sense of agency and depth of knowledge transformation. Through a randomized control trial with 90 undergraduate students, we compare three conditions: (1) a chat-based LLM writing assistant, (2) an integrated AI writing tool to support diverse subprocesses, and (3) a standard writing interface (control). Our findings demonstrate that, among AI-supported conditions, students using the integrated AI writing tool exhibited greater agency over their writing process and engaged in deeper knowledge transformation overall. These results suggest that thoughtfully designed AI writing support targeting specific aspects of the writing process can help students maintain ownership of their work while facilitating improved engagement with content.