IP addresses are meant to be addresses; if you move your address around everyone else has to update their routing tables. To do what you want you probably want to get your own AS Number and actually participate in routing (BGP etc). I've heard of quite small businesses doing that, but not individuals.

I was looking to do this, but it was just too hard. I believe you need to have a company / association of some kind with a VAT number to get registered. The closest I have found is going with the IPv6 tunnels from someone like Hurricane Electric, but speed is a bit limited.

It's a lot easier than you might think to set up a company and get a VAT number (I'm a contractor so have done that already), though it does cost some money (IIRC something like 40 quid).

Yet with only a personal IPv6 block half the world can't access your resources so that's not a reasonable method at this time.

If you control the DNS there's no real need for owning your own IP addresses as you can just change what they point to. That's usually also much faster to do in a pinch than find a new party that will announce your block and convince the old one to stop doing so. That's usually hours if not days in lead time.

Though if you truly care enough about it you'll also want your own DNS servers and own gTLD in order to own the whole chain.

And to serve that private gTLD to others, you'll need a reachable IP address. :)