Walker to count number of child classes and add number to parent classes

I’ve got a walker that counts the number of the class “break” appear in $depth = 1 unordered lists. I need to add this number as a class to each unordered lists parent <li>, but by the time I’ve counted the number of breaks in the child unordered list, the parent list item has already been generated, so I can’t add the class. I’m’ so close to finishing this walker, I’ve got to be missing something really small. Please help!

// mega menu walker
/*
	ONE REMAINING BUG:
	- Need to add class to LI containing mega-menu-columns-#
*/
class megaMenuWalker extends Walker_Nav_Menu {
	private $column_limit = 3; /* needs to be set for each site */
    private $show_widget = false;
	private $column_count = 0;
    static $li_count = 0;
    function start_el(&$output, $item, $depth = 0, $args = array(), $id = 0) {
        $classes = empty($item->classes) ? array() : (array) $item->classes;
        $item_id = $item->ID;
        if ($depth == 0) self::$li_count = 0;
        if ($depth == 0 && in_array("widget", $classes)) {
            $this->show_widget = true;
			$this->column_count++;
        }
		if ($depth == 1 && self::$li_count == 1) {
			$this->column_count++;
		}
        if ($depth == 1 && in_array("break", $classes) && self::$li_count != 1 && $this->column_count < $this->column_limit) {
            $output .= "</ul><ul class=\"sub-menu\">";
			$this->column_count++;
        }
		if ($depth == 0 && $this->column_count > 0) {
			// always returns 0 unless there's a widget
			$mega_menu_class = " mega-menu-columns-" . $this->column_count;
		}
        $class_names = join(" ", apply_filters("nav_menu_css_class", array_filter($classes), $item));
        $class_names = " class=\"" . esc_attr($class_names . $mega_menu_class) . "\"";
        $output .= sprintf(
            "<li id=\"menu-item-%s\"%s><a href=\"%s\">%s</a>",
            $item_id,
            $class_names,
            $item->url,
            $item->title
        );
        self::$li_count++;
    }
    function start_lvl(&$output, $depth = 0, $args = array()) {
        if ($depth == 0) {
			$output .= "<section>";
        }
        $output .= "<ul class=\"sub-menu\">";
    }
    function end_lvl(&$output, $depth = 0, $args = array()) {
        $output .= "</ul>";
        if ($depth == 0) {
            if ($this->show_widget) {
                ob_start();
                dynamic_sidebar("Navigation Callout");
                $widget = ob_get_contents();
                ob_end_clean();
                $output .= $widget;
                $this->show_widget = false;
            }
            $output .= "</section>";
        }
    }
    function end_el(&$output, $item, $depth = 0, $args = array(), $id = 0) {
		if ($depth == 0 && $this->column_count > 0) {
			/* needs to be added to opening level 0 li */
			$column_count_class = " mega-menu-columns-" . $this->column_count;
			$output .= $column_count_class;
			/* end */
			$this->column_count = 0;
		}
        $output .= "</li>";
    }
}