This is really interesting! I just tried visiting a random nytimes article, which was over my free quota (because everyone on HN seems to have subscriptions at every news website).
I then changed the url to nytimes.com. AND IT LOADED! Wow. My free article limit on every website just doubled.
I think in almost every case you can also just clear your cookies for that site after reaching the free limit.
This is much quicker, no?
Private / incognito mode also works for this most of the time. :)
which basically removes cookies and other metadata.