In this paper, we emphasize the importance of looking beyond technology itself and including interactional and experiential elements in our research gaze in informal computing education in science museums. We argue that, in these contexts, facilitation can be understood as "design work" that is both complex and challenging. We identify how focusing on "infrastructuring"--the process by which an exhibit's support systems emerge, shift, and are sustained in practice--can help develop a richer understanding of the complexity of this work. In this study, we examine facilitators' experiences of facilitating and supporting a computational exhibit in a science museum. We identify how facilitators' expertise, roles, and responsibilities shape their facilitation work. Through analysis of video-recorded interactions at the exhibit and interviews with facilitators, we showcase how facilitators' in-the-moment design moves addressed breakdowns of the exhibit's infrastructure. These design moves emerged from the complex interaction of each facilitator's epistemological views of computing and museum education, values, past experiences, and disciplinary background, as well as the museum culture and other institutional constraints. This analysis represents an important challenge to technocentric stances in informal computing education with implications for informal educators and managers, as well as designers and design researchers more broadly.