Running all writing through AI to re-write everything in a different style while conveying the same information might work. Create a way to apply it to all online writing and you have something like a writing VPN.

Exactly. You barely need "AI" for this. Changing style enough to put some sand in a sophisticated text identifier could be as simple as introducing some spelling and grammar variations. It could easily be commoditized (isn't grammarly doing this already minus the privacy part?). Of all cat and mouse games LE and intelligence are playing, for this one I'm betting on the mouse.

Just write all your 'sensitive' texts in leetspeak, use very few words, and very short words and it should be fine. It's like the typing equivalent of cutting letters out of magazines.

I proposed this as an automated process for our provinces social services/inquiries email. The idea being that the text would be harder to use as a method of discrimination.