I have a feeling with a bit of research you could start enough of a lawsuit to convince the website to give up the information for less than $100 a few hours of work.
If they were reluctant their host might well be willing to drop them to avoid being dragged into it.
YOU can probably avoid thousands of dollars in costs by doing a bit of legwork they probably aren't as lucky.
The website in question is owned by the libelous one, so the first idea won't work.
As far as the host, the problem turns into the same one as the IP enforcement has: Kill one head, and two more appear. My slanderer appears to not have a job, so it's no problem for him to keep moving on and getting new hosting. And for the next host he lands on, I've made myself a real target of that website.
Half the time I feel like this is a real problem with UBI proposals -- if we let people have free time all day, a certain fraction is going to waste it with libel or gamergate or SJW stuff, where the people who actually do something with their lives get attacked for no apparent reason. Like, I'm a huge fan of UBI, but without social support for self-worth outside of paid work, it's going to create a whole new set of social problems. Still a more tractable problem than poverty, I'd hope.
If they were reluctant their host might well be willing to drop them to avoid being dragged into it.
YOU can probably avoid thousands of dollars in costs by doing a bit of legwork they probably aren't as lucky.