Counting top level items in a custom menu walker

Calculation you talking about going here:

if( !isset( $this->break_point ) )
        $this->break_point = ceil( $this->current_menu->count / 2 ) + 1;

You can’t get top-level items count this way. Instead you should count it yourself. You can do this using wp_get_nav_menu_items(). Every top-level item should have menu_item_parent set to ‘0’.

You should create additional variable where you calculate already displayed elements. So top of your file should looks like this:

class Split_Menu_Walker extends Walker_Nav_Menu {

    public $break_point = null;
    public $displayed = 0; 

function start_el(&$output, $item, $depth, $args, $id=0) {

    global $wp_query;

    if( !isset( $this->break_point ) ) {
        $menu_elements = wp_get_nav_menu_items( $args->menu );
        $top_level_elements = 0;

        foreach( $menu_elements as $el ) {
            if( $el->menu_item_parent === '0' ) {
                $top_level_elements++;
            }
        }
        $this->break_point = ceil( $top_level_elements / 2 ) + 1;
     }   


    $indent = ( $depth ) ? str_repeat( "\t", $depth ) : '';
...
...
...

Then you should increment $this->displayed++; every time you display top level element (for example at the end of start_el() function):

if( $item->menu_item_parent === '0' ) {
    $this->displayed++;
}

Lastly instead of

if( $this->break_point == $item->menu_order )

you should use

if( $this->break_point == $this->displayed )

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