Oh, I agree that the carrier isn't going to work with just any website.
But companies like Zoom (as would be relevant in this scenario) might hold more sway, especially if the looming threat is "deal with this on your end, or we will, with the blunt instrument that is IP banning". (Now, whether Zoom would engage in an IP ban just for abuse affecting a single school is a different story. But I imagine they must have some motivation to deal with zoombombing. Right??)
The school itself might not have the resources to engage in a legal battle, but they could certainly get law enforcement involved, especially if the abuse enters, say, hate crime territory, as it seems like it may have in this case.
(Granted, the privacy concerns that you raise are an entire issue in themselves, and I don't have any answers there.)
To be clear -- this isn't a novel proposal, per se, unless talking to other people is novel :) But, it's just a suggestion that while circumventing CG-NAT is technologically infeasible from the outside, technical solutions are not the only option.
And if it's not possible from the outside, well, there's one entity who's positioned to further trace the abusive users...