I am sorry to hear that you are experiencing this, DrChaos. I am curious too since I plan to open a public forum some day and know this could become an issue.
However, I had the same issue as yours with our company's board not too long ago and, yes, I kept banning I.P. addresses to no avail. This user would dynamically create new ones and to make matters worse, would post everything in gibberish.
Our forums are different, however. First, a visitor must pay to be on the site with a user/password. Then, they are required to create a user/password to access the community. We have a double barrier. Nonetheless, it came down to our tech people to finally ban this person by banning a couple of different things.
Not only could we ban the credit card, but they banned anyone that attempted to post anything with a combination of variables such as matching I.P.'s, workstations, operating systems, addresses, ISP services, etc. We have not seen this person for over 8 months.
Barring any great advice from here on threadsdev, you might have some luck with your hosting provider. Just a thought... small one, but all I can offer at the moment. Good luck.