Involving stakeholders throughout the creation of new educational technologies can help ensure their usefulness and usability in real-world contexts. However, given the complexity of learning analytics (LA) systems, it can be challenging to meaningfully involve non-technical stakeholders throughout their design and development. This article presents a detailed case study of the iterative co-design of Lumilo, a wearable, real-time learning analytics tool for teachers working in AI-enhanced K-12 classrooms. In the process, we argue that the co-design of LA systems requires "new kinds of prototyping methods." We introduce one of our own prototyping methods, REs, to address unique challenges of co-prototyping data-driven algorithmic systems such as LA tools. This work presents the first end-to-end demonstration in the literature of how non-technical stakeholders can participate throughout the whole design process for a complex LA system -- from early generative phases to the selection and tuning of analytics to evaluation in real-world contexts. We conclude with a summary of methodological recommendations for future LA co-design efforts.