Update on Custom Post Template plugin:
I have found that if you are using only your custom post type and not the standard post type, then a quick fix is to change ‘post’ in line 48 of custom-post-templates.php (the add_meta_box line) to the name of your post type.
My configuration doesn’t need to use the standard post types, and I only want custom post templates for my custom post type. I don’t know enough php to make it show up on both at once, but does anyone know how that is done? Here is the line of code:
$this->add_meta_box( 'select_post_template', __( 'Post Template', 'custom-post-templates' ), 'select_post_template', 'post', 'side', 'default' );