Turns out you can use this filter to alter the priority of the post_status links:
$views = apply_filters( "views_{$this->screen->id}", $views );
If your custom post type is ‘inbound-email’ then the applied filter will look like this:
add_filter( 'views_edit-inbound-email' , 'function_to_filter_priority' );
/**
* rebuild priority of post status links
* @param ARRAY $links
* @return ARRAY $new_links
*/
function function_to_filter_priority( $links ) {
$new_links['all'] = $links['all'];
if (isset($links['draft'])) {
$new_links['draft'] = $links['draft'];
}
if (isset($links['pending'])) {
$new_links['pending'] = $links['pending'];
}
if (isset($links['sent'])) {
$new_links['sent'] = $links['sent'];
}
if (isset($links['automated'])) {
$new_links['automated'] = $links['automated'];
}
if (isset($links['trash'])) {
$new_links['trash'] = $links['trash'];
}
return $new_links;
}