After posting this question over six months ago, I've continued to play with the iNotes template.
Turns out the real solution to my original problem boils down to two things:
First, virtually any view or folder you want to open in the iNotes template gets opened via a $$ViewTemplate, and there's a $$ViewTemplate Default that was the direct cause of the heartburn I'd mentioned in my original post.
Secondly, the trick that Stephan mentioned solves the rest of the problem. Add &ui=webmail to the URLs you build.
I've got this slightly better documented (and a sample to play with) here: