Spotify at least does allow you to add local files on a computer, and they even sync tracks to your phone when they are on an offline playlist when the devices are on the same network. I’ve done that myself to get some otherwise unavailable songs into my catalogue, and am thinking of starting the move to owning all my music that way
If you were using the default port 25565, you could simply have a DNS A record pointing to the server IP. But since that is not the case, you have to additionally set up a SRV record in your DNS. NOIP describes what this is and how to set it up on their service here, but it will of course differ for your DNS provider.
This still requires that the Minecraft server port is directly accessible from the other clients, but it sounds like that is not the problem