Magento – Get product video

I have added some videos to my product via the add video section under product "Images And Videos". I want to be able to display the videos added this way in a custom section. The code currently looks like this:

$images = $full_product->getMediaGalleryImages();
foreach($images as $image){
  if(in_array($image->getFile(), $used_images)){
    continue;
  }
  ?>
  <li>
    <?php
    if($image->getMediaType() == "external-video") { 
      ?>
      <iframe width="640" height="480" src="<?php echo $image->getVideoUrl(); ?>" frameborder="0" allowfullscreen></iframe>
      <?php
    } else { // general show an image
    ?>
      <img src="<?php echo $image->getUrl(); ?>" alt="<?php echo $_productNameStripped; ?>" />
    <?php } ?>
  </li>
<?php } ?>

I want to display only certain images and videos in the list (hence the $used_images bit), so far it is working fine except the getVideoUrl for youtube returns me a wrongly formatted youtube url.

I get:
https://www.youtube.com/watch?v=abcdefghij

but I need:
https://www.youtube.com/embed/abcdefghij

It's possible for me to write some php code that would pull out the video code and get me the correct url but I want to know if their are magento methods for this or displaying videos/iframes. Creating my own methods shortcut here might cause me problems with other magento features (such as vimeo videos) not working in this display.