Actually this can be done. It's not pretty. If you are in a bind and just need to get this done you can hijack the MyPageOrder plugin to work with your Custom Post Type. The one caveat is you Custom Post Type must be based on Pages not Posts. In other words you should set the 'capability_type' => 'page' when setting up your Custom Post Type. For non-Page based Custom Post Types the order defaults to post_date like for Posts.
Here are the steps to changing MyPageOrder for a one time use to order your 80+ items.
1. First download, install and activate the MyPageOrder plugin.
2. Next you will need to edit the plugin PHP code. All changes are made in one file /plugins/my-page-order/mypageorder.php. Once you have the PHP file open search for the term 'post_type'. You should find three references which is set to 'page'. Change this to your Custom Post Type. Then save the file.
3. Now when you navigate to the My Page Order page under Pages you will see a listing of your Custom Post Types.
Again this is a temporary solution.