Hmmmm, the solution to this problem was to read the details of the plugin. It has the capability of returning values other than a link to the next post – this includes the ID of the Next and Previous Post.
In case anyone else reads this in the future and wants to see how to get the ID all you have to do is something like:
<?php $link=next_post_link_plus( array('order_by' => 'custom', 'meta_key' => 'Sort Number','return'=>'id') );?>
Then you can recover any information that you need from the post.