Seems we are talking different issue, your first screenshot
http://d7j863fr5jhrr.cloudfront.net/wp-content/uploads/Screen_Shot_2013_05_23_at_9.37.38_AM.png
select posts from a custom post type "featured project".
The screenshot:
http://d7j863fr5jhrr.cloudfront.net/wp-content/uploads/Screen_Shot_2013_05_28_at_10.37.52_AM.png
the "link URL" is a custom field of post type "media",
Are you going to select posts from a custom post type "featured project", and display the link from the field "link URL"?
If isn't, please describe detail steps to duplicate same problem, I need test it in my localhost.
Thanks