If the crawlers refuse to voluntarily respect your robots.txt, then you are well within your rights to poison their data.
Sue for $180,000 per infringement which should be calculated for each illegal API call.
A person should be able to write in a terms of use or license page on their website that says "do not include any content from this website in your AI training data. if you do you will be billed $100 billion dollars." And it should be enforceable. It just turns out that nerds like to say "oh that would be too hard or too expensive, so we're going to ignore it."
Unauthorized access, system damage, and maybe even extortion all apply here.