Well we managed to get the permissions to view and edit files that apache creates, but it still leaves a problem when it comes to user file uploads. When someone tries to upload something, the folder # is created, but the file isn't uploaded as the following error is returned:
Unable to create directory /wp-content/blogs.dir/5/files/. Is its parent directory writable by the server?
Manually creating # folder, but not the files folder results in the following:
The uploaded file could not be moved to the upload folder.
If I manually create the folders #/files/, then the user can upload without a problem (as the folder's ownership is no longer Apache's). I tried looking for a solution, but the only thing returned was stuff like setting permissions to 777 or recursively changing ownership... This isn't ideal, since you still have to do this for every new user added.
Another thing I noted was that it's impossible to change the upload path for an individual blog, no matter if I modify the settings under the edit blog options.