Breastfeeding is not only a public health issue, but also a matter of economic and social justice. This paper presents an iteration of a participatory design process to create spaces for re-imagining products, services, systems, and policies that support breastfeeding in the United States. Our work contributes to a growing literature around making hackathons more inclusive and accessible, designing participatory processes that center marginalized voices, and incorporating systems-and relationship-based approaches to problem solving. By presenting an honest assessment of the successes and shortcomings of the first iteration of a hackathon, we explain how we restructured the second Make the Breast Pump Not Suck hackathon in service of equity and systems design. Key to our re-imagining of conventional innovation structures is a focus on experience design, where joy and play serve as key strategies to help people and institutions build relationships across lines of difference. We conclude with a discussion of design principles applicable not only to designers of events, but to social movement researchers and HCI scholars trying to address oppression through the design of technologies and socio-technical systems.