I stitched together your excellent work with another plugin by Birgire to use the WP playlist for external files. This can be found at https://wordpress.stackexchange.com/questions/141766/making-audio-playlist-with-external-audio-files.
Somewhere in your file around line 56, remove the loop you’re doing and replace it with this, which basically takes all of those mp3 files and wraps them into a shortcode to be handled by the Birgire plugin. Of course this could be implemented more elegantly, and/or your admin interface could offer the Playlist format leveraging if the Birgire plugin is active, etc.
// We just define a default icon that is handy; we have some favicons at root:
$image = '/apple-icon-72x72.png';
// create an array for output:
$output = array();
?>
<ul class="podcast_feed">
<?php if ( $maxitems == 0 ) : ?>
<li><?php _e( 'No items', 'dkpp-domain' ); ?></li>
<?php else :
foreach ( $feed_items as $item ) :
if ($enclosure = $item->get_enclosure()) {
$audio = $enclosure->get_link();
}
$title = $item->get_title();
$description = addslashes( wp_trim_words(strip_tags($item->get_description()), 14, '...' ) );
$output[] = "[wpse_trac src='$audio' title='$title' meta_album='$description' thumb_src='$image' ]";
endforeach; ?>
<?php endif;
// build off our shortcode and then do it:
// sort it if you want: asort($output);
// build a shortcode using Birgire's plugin: WPSE Playlist found on Github
$output = '[wpse_playlist type="audio" tracklist="true" tracknumbers="false" images="true" artist="true"]' .
implode('', $output).
'[/wpse_playlist]';
if (class_exists( '\birgire\Playlist' )) { echo do_shortcode($output); }
else {echo "You need to have Birgire's plugin from https://github.com/birgire/wpse-playlist activated.";}
?>
</ul>
<?php echo $args['after_widget'];
