As I was interested into porting some features of my myCourses and my siteNavigation Blocks to Moodle 2.x, I dived into the navigation code of Moodle 2.x Unfortunately it is deepley nested and hooked into the big bib object called $PAGE, so I see only little chances of making changes/enhancements there unless a thorough understanding of the code would allow me to do so. But I might be faster in developing again my own sitenavigation Block for 2.x
As the $PAGE object is complex and big, I could really imagine that a lot of caching is involved there, even with the whole navigation, where myCourses are integrated, so as not to render the whole tree on every Moodle-Course-Page you visit. This makes sense and would explain why you have a certain delay here.
I have no time to dive into that code again, maybe you do it yourself.
Rosario