Just some thoughts before I start my sleep interval :)

Plugins are great, especially because each can request individual permissions. That way, users don't get scared away by permission requests. Some example code here.

Widget: yes, 1x1 [start|end|track|new_event|happy] button would probably be best. One can arrange those as they see fit.

Ordinal values: perhaps just an autocomplete option for event labels.

As for analytics, perhaps draw selected intervals above each other with selected tracks plotted over them (each with own scale) and vertically write labels of (selected?) events. This may be messy, but can be done later and elsewhere (e.g. Google charts, if they can be combined). Also, setting up icons for events/ordinals would be nice.