Many people use health tracking apps to keep track of their menstrual cycles, often in the hopes of better understanding their own health, and being able to identify when something might be wrong. However, it can be very difficult to interpret this data alone. Meanwhile, it is becoming increasingly common for researchers to use data from these apps to learn more about menstrual health. In this work we ask, how could more participatory approaches to conducting menstrual health research benefit both participants and researchers? We identify key challenges and risks of this kind of engagement, and propose four design guidelines for human-in-the-loop data analysis tools that engage participants with large-scale, quantitative menstrual health research: surface and elicit feedback on the data cleaning and analysis procedure; convey information relative to other users and clinical guidance; structure engagement to ensure valid analyses; and support social engagement and learning. For each of these, we highlight key open research questions relevant to the HILDA and visualization research communities. We plan to for evaluate and iterate on these guidelines through design workshops with users, researchers, and healthcare providers.