You can get the NYT literally delivered to your door in completely offline form. I used to pick up a copy to read during lunch at work, back before smartphones.
I'd point to something like Feedbin's ability to pull remote content from the subscribed site, then. No idea how well it works on something with an e-ink display, though. You might look whether anyone's made a stand-alone RSS client aimed at offline reading that has that ability.
The Sunday NYT is a bit of a challenge, mind you.