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Designing patient-collected health data visualizations to support discussing patient data during clinical visits is a challenging problem due to the heterogeneity of the parties involved: patients, healthcare providers, and healthcare systems. Designers must ensure that all parties' needs are met. This complexity makes it challenging to find a definitive solution that can work for every individual. We have approached this research problem -- communicating patient data during clinical visits -- as a wicked problem. In this article, we outline how wicked problem characteristics apply to our research problem. We then describe the research methodologies we employed to explore the design space of individualized patient data visualization solutions. Last, we reflect on the insights and experiences we gained through this exploratory design process. We conclude with a call to action for researchers and visualization designers to consider patients' and healthcare providers' individualities when designing patient data visualizations.