Not the exact same problem, but a few months ago, I tried to block youtube traffic from my home (I was writing a parental app for my child) by IP. After a few hours of trying to collect IPs, I gave up, realizing that YouTube was dynamically load-balanced across millions of IPs, some of which also served traffic from other Google services I didn't want to block.
I wouldn't be surprised if it was the same with LLMs. Millions of workers allocated dynamically on AWS, with varying IPs.
In my specific case, as I was dealing with browser-initiated traffic, I wrote a Firefox add-on instead. No such shortcut for web servers, though.