Pagination for custom taxonomy 404

I have a custom post type case-study which I have a number of taxonomies registered. I was looking to create the following URL structure:

• Archive: domain.com/post_type/
• Taxonomy: domain.com/post_type/tax_name/
• Post: domain.com/post_type/post_name/

The reasoning behind this is that a single post can have multiple taxonomies.

The issue I have is that on the taxonomy page, when I list out the related posts, if I use the posts_nav_link() it works for the main archive page, but returns a 404 for each taxonomy, with the exception on one.

Here is how I’ve registered the post type:

function viamo_register_post_types() {
    $case_studies_labels = array(
        'name'                => __( 'Case Studies', 'viamo' ),
        'singular_name'       => __( 'Case Study', 'viamo' ),
        'add_new'             => _x( 'Add New Case Study', 'viamo', 'viamo' ),
        'add_new_item'        => __( 'Add New Case Study', 'viamo' ),
        'edit_item'           => __( 'Edit Case Study', 'viamo' ),
        'new_item'            => __( 'New Case Study', 'viamo' ),
        'view_item'           => __( 'View Case Study', 'viamo' ),
        'search_items'        => __( 'Search Case Studies', 'viamo' ),
        'not_found'           => __( 'No Services found', 'viamo' ),
        'not_found_in_trash'  => __( 'No Services found in Trash', 'viamo' ),
        'parent_item_colon'   => __( 'Parent Service:', 'viamo' ),
        'menu_name'           => __( 'Case Studies', 'viamo' ),
    );
    $case_studies_args = array(
        'labels'              => $case_studies_labels,
        'hierarchical'        => false,
        'public'              => true,
        'show_ui'             => true,
        'show_in_menu'        => true,
        'show_in_admin_bar'   => true,
        'menu_position'       => null,
        'menu_icon'           => 'dashicons-awards',
        'show_in_nav_menus'   => true,
        'publicly_queryable'  => true,
        'exclude_from_search' => false,
        'has_archive'         => 'case-studies',
        'query_var'           => true,
        'can_export'          => true,
        'rewrite'             => array( 'slug' => 'case-studies' ),
        'capability_type'     => 'post',
        'supports'            => array('title', 'thumbnail', 'editor', 'revisions')
    );
    register_post_type( 'case-study', $case_studies_args );
}
add_action( 'init', 'viamo_register_post_types' );

The taxonomies are then registered as follows:

function viamo_register_taxonomomies() {
    $sector_labels = array(
        'name'                   => _x( 'Sectors', 'Taxonomy plural name', 'viamo' ),
        'singular_name'          => _x( 'Sector', 'Taxonomy singular name', 'viamo' ),
        'search_items'           => __( 'Search Sectors', 'viamo' ),
        'popular_items'          => __( 'Popular Sectors', 'viamo' ),
        'all_items'              => __( 'All Sectors', 'viamo' ),
        'parent_item'            => __( 'Parent Sector', 'viamo' ),
        'parent_item_colon'      => __( 'Parent Sector', 'viamo' ),
        'edit_item'              => __( 'Edit Sector', 'viamo' ),
        'update_item'            => __( 'Update Sector', 'viamo' ),
        'add_new_item'           => __( 'Add New Sector', 'viamo' ),
        'new_item_name'          => __( 'New Sector Name', 'viamo' ),
        'add_or_remove_items'    => __( 'Add or remove Sectors', 'viamo' ),
        'choose_from_most_used'  => __( 'Choose from most used Sector', 'viamo' ),
        'menu_name'              => __( 'Sectors', 'viamo' ),
    );
    $sector_args = array(
        'labels'            => $sector_labels,
        'public'            => true,
        'show_in_nav_menus' => true,
        'show_admin_column' => false,
        'hierarchical'      => true,
        'show_tagcloud'     => true,
        'show_ui'           => true,
        'query_var'         => true,
        'rewrite'           => array( 'slug' => 'case-studies'),
        'query_var'         => true,
        'capabilities'      => array(),
    );
    register_taxonomy( 'sector', array( 'case-study'), $sector_args );

    $locations_labels = array(
        'name'                  => _x( 'Locations', 'Taxonomy plural name', 'viamo' ),
        'singular_name'         => _x( 'Location', 'Taxonomy singular name', 'viamo' ),
        'search_items'          => __( 'Search Locations', 'viamo' ),
        'popular_items'         => __( 'Popular Locations', 'viamo' ),
        'all_items'             => __( 'All Locations', 'viamo' ),
        'parent_item'           => __( 'Parent Location', 'viamo' ),
        'parent_item_colon'     => __( 'Parent Location', 'viamo' ),
        'edit_item'             => __( 'Edit Location', 'viamo' ),
        'update_item'           => __( 'Update Location', 'viamo' ),
        'add_new_item'          => __( 'Add New Location', 'viamo' ),
        'new_item_name'         => __( 'New Location Name', 'viamo' ),
        'add_or_remove_items'   => __( 'Add or remove Locations', 'viamo' ),
        'choose_from_most_used' => __( 'Choose from most used Location', 'viamo' ),
        'menu_name'             => __( 'Locations', 'viamo' ),
    );
    $locations_args = array(
        'labels'            => $locations_labels,
        'public'            => true,
        'show_in_nav_menus' => true,
        'show_admin_column' => false,
        'hierarchical'      => true,
        'show_tagcloud'     => true,
        'show_ui'           => true,
        'query_var'         => true,
        'rewrite'           => array( 'slug' => 'case-studies'),
        'query_var'         => true,
        'capabilities'      => array(),
    );
    register_taxonomy( 'location', array( 'case-study'), $locations_args );

    $service_labels = array(
        'name'                  => _x( 'Services', 'Taxonomy plural name', 'viamo' ),
        'singular_name'         => _x( 'Service', 'Taxonomy singular name', 'viamo' ),
        'search_items'          => __( 'Search Services', 'viamo' ),
        'popular_items'         => __( 'Popular Services', 'viamo' ),
        'all_items'             => __( 'All Services', 'viamo' ),
        'parent_item'           => __( 'Parent Service', 'viamo' ),
        'parent_item_colon'     => __( 'Parent Service', 'viamo' ),
        'edit_item'             => __( 'Edit Service', 'viamo' ),
        'update_item'           => __( 'Update Service', 'viamo' ),
        'add_new_item'          => __( 'Add New Service', 'viamo' ),
        'new_item_name'         => __( 'New Service Name', 'viamo' ),
        'add_or_remove_items'   => __( 'Add or remove Services', 'viamo' ),
        'choose_from_most_used' => __( 'Choose from most used Service', 'viamo' ),
        'menu_name'             => __( 'Services', 'viamo' ),
    );
    $service_args = array(
        'labels'            => $service_labels,
        'public'            => true,
        'show_in_nav_menus' => true,
        'show_admin_column' => false,
        'hierarchical'      => true,
        'show_tagcloud'     => true,
        'show_ui'           => true,
        'query_var'         => true,
        'rewrite'           => array( 'slug' => 'case-studies'),
        'query_var'         => true,
        'capabilities'      => array(),
    );
    register_taxonomy( 'service', array( 'case-study' ), $service_args );
}
add_action( 'init', 'viamo_register_taxonomomies' );

Following an article I read to achieve my desired URL’s I then use the following function to extend the generate_rewrite_rules hook:

function generate_taxonomy_rewrite_rules( $wp_rewrite ) {
    $rules      = array();
    $post_types = get_post_types(array('name' => 'case-study', 'public'   => true, '_builtin' => false ), 'objects');
    $taxonomies = array(
        'sector'   => get_taxonomies(array('name' => 'sector', 'public'   => true, '_builtin' => false ), 'objects'),
        'service'  => get_taxonomies(array('name' => 'service', 'public'  => true, '_builtin' => false ), 'objects'),
        'location' => get_taxonomies(array('name' => 'location', 'public' => true, '_builtin' => false ), 'objects')
    );

    foreach ( $post_types as $post_type ) {
        $post_type_name = $post_type->name; // 'case-study'
        $post_type_slug = $post_type->rewrite['slug']; // 'case-studies'

        foreach ( $taxonomies as $key => $taxonomy ) {
            $taxonomy = $taxonomy[$key];

            if ( $taxonomy->object_type[0] == $post_type_name ) {
                $terms = get_categories( array( 'type' => $post_type_name, 'taxonomy' => $taxonomy->name, 'hide_empty' => 0 ) );
                foreach ( $terms as $term ) {
                    $rules[$post_type_slug . '/' . $term->slug . '/?$'] = 'index.php?' . $term->taxonomy . '=' . $term->slug;
                }
            }
        }
    }
    $wp_rewrite->rules = $rules + $wp_rewrite->rules;
}
add_action('generate_rewrite_rules', 'generate_taxonomy_rewrite_rules');

To clarify the following URLs work:

1. domain.com/case-studies/page/2/ (this is the main post-type archive pagination)
2. domain.com/case-studies/service_1/page/2/ (this is a taxonomy which is registered last)

And these 404:

1. domain.com/case-studies/sector_1/page/2/ (this is a taxonomy which is registered first)
2. domain.com/case-studies/location_1/page/2/ (this is a taxonomy which is registered second)

From the attempts I’ve made to fix this, I believe each of the rewrites (during the taxonomy registration) are overwriting those made registered before it. Because if I re-order the taxonomies that are registered the last one is always the one where pagination works correctly.

How can I set the taxonomy rewrites so that pagination works for each taxonomy?