Sub-directory install preventing uploads

Before I begin, I have already: searched google, the forums, and stackoverflow. This isn’t a case of my host preventing uploads because of chmod or permissions. This is wordpress itself being confused about how my installation is structured.

This is a strange case where I know exactly what is wrong but have no clue how to fix it. I recently transferred a localhost installation of wordpress to my live site with no issues. I used a sub-directory installation (www.site.com/wordpress/) but modified the home/site url values in index.php, wp-config.php, and .htaccess to allow “www.site.com” to direct to “www.site.com/wordpress/” without displaying it. All my permalinks are working correctly and everything is fine except one thing.

Images being uploaded return the error:
“photo (1).JPG” has failed to upload due to an error
The uploaded file could not be moved to wp-content/uploads/2014/06.

Obviously, that folder doesn’t exist because it’s really in /wordpress/wp-content/uploads/2014/06.

So how do I make it so the wordpress media uploaded recognizes that the actual installation is in my /wordpress/ folder? Everything else in the admin panel recognizes that while the Home URL says otherwise, the actual site location is not contained within the root directory.

It’s still possible for me to upload images via FTP, but that does not automatically create the thumbnail, small, medium, and large versions.