Scientific writing, in the form of lab notebooks, proposals, and reports, is a common element of physics lab classes. Multiweek student-designed projects are growing in popularity, especially in advanced lab courses, and writing may play a unique role in these types of courses. In prior work, we developed a framework of possible goals for writing in physics lab classes. Here, we use that framework as a lens through which to view three different advanced lab courses that include student-designed projects. We conduct a multiple case-study analysis to investigate how these courses incorporate writing to address various goals. We find that both the timescale and the open-ended nature of projects present unique opportunities for having students engage in authentic writing practices.