Funnily enough, self hosting is why I can't use IPv6. I want vlan isolation, but only get a /64 from my ISP.
Fortunately the lack of IPv6 also isn't a meaningful loss anyway so whatever
You could put your server at x::1 and static-route that address as a /128 on your router, if it supports it. The reverse route might be a bit tricky but putting ::0 on the router and telling the server it's a /127 should work. Anything outside of the /127 (so, all the randomly generated addresses on your home network) would go back through the router.
Now if that /64 is also changing every day, then it's a problem and idk what you'd do.