Oh yes, I remember them. Every few years I remember the Badger song and play it for a while + some other catchy old Weebl’s stuff like Amazing Horse, Where can you see lions (only in Kenya)… Oh god, the more I think about them the more I remember.
Apparently Badger Badger is from 2003.
Caramelldansen (gif + music) is from 2005.
Daft Hands from 2007.
Dancing Baby is even older, from 96 / 97.
Self hosting doesn’t mean you should host everything yourself at home, using a VPS you manage (so the data inside it is still yours) is also a viable option for selfhosting. I myself host some services at home and a few others in a VPS.
As for Dyndns, I’ve used a few providers over the years. DuckDNS is the one I’ve been using for 5 years or so and it’s not failed me once. Pretty happy with it.
Maybe you could have a duckdns pointing to your dynamic IP and your domains / subdomains with a CNAME pointing to the dyndns address?