Nice work and nice writeup. It's interesting to me how strongly the design of original radar displays anchors the project. Your toddler might never interact with a real CRT, much less an ASR-9 with a PPI display. But you've gone to great lengths to simulate one for her.
Partly because of your affinity for skeumorphism, as you said, but it may also be because the OG radar display is a fantastic distillation of "Is there something in the sky and where is it relative to me?" All the UIs we have for sky-watching now have moved away from that in favor of contextual data or linking out to other services (or creating space to display ads). In the process of presenting all that additional information, they've lost the ability to easily answer that particular question.