I simply stop a NYT or WaPo article from loading the paywall, after the article appears. Pretty easy to do, once you get used to the timing. One of the few advantages of having a slow internet connection.
NYTimes is easier as you can reload an article multiple times if you miss the right cutoff point. Reloading on WaPo takes you to the homepage and makes you search for and click the link again.
Also, generally articles are not exclusive to NYT or WaPo, so you can just copy the headline and run a search, and usually find the article on a free site. Takes an extra 10 secs usually. Sometimes I can even find a longer version instead of the NYT edited/truncated version (usually a few extra paragraphs of details towards the end).