Add a TinyMCE Core Plugin Using tiny_mce_before_init

Sorry to answer my own question, but of course I figured it out right after posting this. Instead of tiny_mce_before_init I needed to use mce_external_plugins. Also, I had to download TinyMCE from their website and copy the plugins/advlist folder to WordPress. I created a folder called mce in my WordPress plugins directory and pasted the advlist folder into there.

function my_mce_external_plugins( $plugin_array ) {
    $plugin_array['advlist'] = plugins_url() . '/mce/advlist/plugin.min.js';
    return $plugin_array;
}
add_filter( 'mce_external_plugins', 'my_mce_external_plugins' );