> But if you are like me and your Raspberry Pi is sitting behind your router's firewall, you can't use this approach as your IP-address is changing all the time.

If your DNS provider has an easily usable API, you can set up something that checks your current public ipv4/v6 address and changes the DNS record if the IP address changes. You just need to set the DNS TTL to something smaller, such as 1 hour or less, to limit the impact of a changing IP address.