Universities have been forced to rely on remote educational technology to facilitate the rapid shift to online learning. In doing so, they acquire new risks of security vulnerabilities and privacy violations. To help universities navigate this landscape, we develop a model that describes the actors, incentives, and risks, informed by surveying 105 educators and 10 administrators. Next, we develop a methodology for administrators to assess security and privacy risks of these products. We then conduct a privacy and security analysis of 23 popular platforms using a combination of sociological analyses of privacy policies and 129 state laws, alongside a technical assessment of platform software. Based on our findings, we develop recommendations for universities to mitigate the risks to their stakeholders.