What I ended up doing was setting up three sidebars, each using an instance of Advanced Menu Widget and settings as follows:
Sidebars
1. main nav: start at level 0, display 1 level deep, display all items
2. second level nav: start at level 1, display 2 level deep, only show strictly related sub items
3. third level nav: start at level 2, display 3 level deep, only show strictly related sub items
This gives me pretty much the control I needed.