More or less.
What I ended up doing was get a list of the menu items that listed the categories (Assignments, Syllabus, etc.). Then I looped through each menu item. For each menu item, I added a query argument for the course tax term using add_query_arg() to the menu item’s url property. Finally, I output the menu as I wanted it to display. It might not be the most elegant solution, but it worked remarkably well. The category was filtered by the course tax term. That’s the more part. The less part is that only the most recent posts for a given category are displayed, per the settings in the admin. I didn’t catch that until I had more assignments than my setting was set to display. I either need to paginate or force all the posts to display. Or at least all the posts for a given quarter and paginate the rest.
Here is the code I used:
$course_resources_menu_items = wp_get_nav_menu_items( 'xx' );
<?php foreach ( $course_resources_menu_items as $item ) {
$title = $item->title;
$url = add_query_arg( 'course', $term->slug, $item->url );
echo '<li><a href="' . $url . '" title="' . $title . '">' . $title . '</a></li>';
}; ?>
