Serviio

Network shares aren't showing up in the Library interface. When you click on /Volumes, you only see the physical hard drives. The drive I am trying to use is mounted and accessible. If you manually enter /Volumes/"share name", that doesn't work either. The drive is mounted using SMB protocol. SMB paths and UNC paths do not work either.

Please advise.

I am not a Mac User running serviio, so my knowledge here is limited.
However I guess that serviio runs as a non priviledged user or at least as a different user then you on MacOSX.
Try to find out if you can run the serviio process under your user.
Another thing are the security settings of newer versions of MacOSX. For example if you use terminal on MacOSX and try to access a file outside your user account, MacOSX will ask you if terminal is allowed to access all files. This will apply also to any other process. If you know the process serviio is running under, go into the security settings, an try to drag and drop this process into the access all files category.

I've tried using network shares under Linux, and it doesn't work either. What I had to do was mount the remote shares to the local file system, and then Serviio could see and access the media. Using a network share was not successful. It's been a while since I tried it, but I doubt anything has changed in that respect.