There is an answer to the question - albeit that the community may find this offensive. I don't know why, save cost, that the path has not been taken more often.
Send a cease and desist letter to the individual who is trespassing on your site, and who is violation Title XVIII of the US Code, Tampering with Computers, Fraud and Abuse.
If they don't cease, pony up the cash and sue. In the mid 1990's I had the first case in the WDMO where the sole ISP for the Kansas City area was hacked by 3 teens. I contacted the families (they had rooted one of the servers and were stupid enough to store their application to join "Warez" groups with their real names and addresses in a hidden subdirectory) and asked them to stop the adolescent boys from doing this. They refused.
In a 54 page complaint I had to explain: ISPs, Internet, exceeding access, etc. to a newly appointed judge.
I was more than an advocate, an account of mine had been accessed (thank god, not a client account - The Rust List) and I was ticked off. I charged the parents (only way to go where defendants were minors in a civil action) and stated that the parents had placed a dangerous instrumentality into the hands of minors without adequate supervision and that the minors had engaged in the transfer of stolen software, and kiddie porn (Yep, 16 year old boys taking pictures of their 16 year old GF's is "kiddie porn"). I hit the homeowner's policies and I had a remedy that the courts in those days would not even consider: a lifetime ban on the use of computers for the teenagers.
It got settled within a week of the transfer of discovery.
You have tried everything else: hammer this little shit with a walletectomy. Be careful to pick an attorney who knows what this is and not one associated with a "big firm" where you will be billed to death.
Consider how a court order precluding the jerk from accessing your site might work:
S/He's banned - you find an IP address of his/her violating the Court Order - send it to your attorney and s/he files a motion with the Court showing violation of the Order and the Court will respond with a Show Cause Order why the defendant should not be held in contempt of court.
An attack from other sites/IP addresses start coming in - tell your counsel - and the response can include mirroring the defendants computers, an injunction stopping the defendant from all access to the Internet, and, upon finding that the defendant violated the order by proxy, the Court will impose sanctions.
Ultimately, the jerk may have confined himself to forever be blocked from the Internet. If you are truly pissed off after all of this and you want to be certain that the defendant is off the Internet, hire a PI to follow the defendant for a week or ten days (not cheap) and if s/he is accessing the Internet from a Starbucks - or McD's you have them: back to the judge.
The ultimate Order is beyond belief and will only happen with overwhelming evidence that the defendant had routinely violated the court's orders: no smart phones, no VOIP, no cable or sat TV (Internet is available and s/he has shown a total disregard for the law, so nothing that they can hack to gain access is permitted), no Internet (it would be nice if it were a lifetime ban - likely not), no Internet of things, and ultimately, no computing devices.
If the defendant was making their living in the tech sector - they have ditches to dig and burgers to flip.
That's how to end this with the nuclear option.