I have never built a theremin, but the schematics look straightforward. Then just have to figure out how to make it sensitive enough to detect the rise and fall of a tiny human's chest/back. Then sound an alarm if the breathing stops. SIDS is a terrible thing, and although the cause isn't known, it's generally agreed that the babies just fall into such a deep sleep that they forget to breath. Hopefully this could prevent that
Cool idea! Hope you update this project soon. Let me know if you need help, I've done a lot of work with cap sensors.