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

Even though many phone plans today have unlimited texts, some still don’t. A delivery report is basically a second SMS, that you then have to pay for, so I think that is why it is an opt-in feature.