Note: For anyone landing on this page from Google looking to automatically upload the NYT crossword to your Supernote or similar e-ink tablet, I'm afraid this solution requires some knowledge of programming.
Update 1/12/22: This can be easily adapted to work for the Wall Street Journal crossword as well. Unlike the NYT crossword, the WSJ crossword does not require a paid membership. Scroll down to the bottom of this page for more info.