I had never anything to do with this topic and have no expertise in legal topics but it sounds like you are referring to the Child Protection and Obscenity Enforcement Act [1]. I didn't read the entire thing but just searched for parts talking about keeping records, mostly § 75.2 [2]. Maybe I am interpreting the letters of the law a bit naively but I can not find anything that would require keeping this information anywhere close to the servers used for streaming. Quite to the contrary, it seems to me that you could keep the required records on paper if you wanted to - more or less a copy of the ID, name and aliases used by the performer, and a list of works the performer appears in, for example the URL a stream is available at. But maybe I missed something important.

[1] https://en.wikipedia.org/wiki/Child_Protection_and_Obscenity...

[2] https://www.law.cornell.edu/cfr/text/28/75.2