Good old honeytrap. I’m not sure, but I think that it’s doable.
Have a honeytrap page somewhere in your website. Make sure that legit users won’t access it. Disallow crawling the honeytrap page through robots.txt.
Then if some crawler still accesses it, you could record+ban it as you said… or you could be even nastier and let it do so. Fill the honeytrap page with poison - nonsensical text that would look like something that humans would write.