If Emby is using the Media Server (DLNA) structure to provide access then you can adjust this structure using Custom styles in Media Server.
I have a Custom menu style in Media Server that stops access to photos and movies (each type has one menu item and that points to an unused folder), plus the music menus have additional items to serve specifically from my ALAC (Apple's version of FLAC) folder and also reorder items to my preference.
Regarding Plex as the winner for media accessed from everywhere:
I have't enabled direct Internet access to the Plex Media Server since this has my personal use content yet the authentication is via Plex website (I have no desire to accidentally share this content and invoke any rights vs fair-use questions). Instead I use a VPN back to home for Plex, but do have Audio Station, Video Station, and Moments accessible from the Internet with their NAS authenticated users.
I may be paranoid, but as I said before .... whatever works for you
