Yeah nyt isnt supported right now. Highly encourage you to try https://cup.aihedy.com/en-US/firefox/addon/bypass-paywalls-test

They do more client side "stuff" to bypass more paywalls. This was mostly made as a proof of concept. Thanks for trying it out though. (it does work on sites where they let the google crawler cache the web page)

edit: nyt is now fully supported.