How do I find a way to create a global single.php for a custom post type?

There re various filters you can use to inject your custom template. One being the template_include, the other single_template, and even type_template.

The easiest one would be single_template in your case (example from codex):

function get_custom_post_type_template($single_template) {
     global $post;

     if ($post->post_type == 'my_post_type') {
          $single_template = dirname( __FILE__ ) . '/post-type-template.php';
     }
     return $single_template;
}
add_filter( 'single_template', 'get_custom_post_type_template' );