Embed hints into NYT website itself
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overscore
This may very well be beyond the scope of what you're trying to achieve, but I think it would be very cool to have the hints on the website itself (through a browser extension). For example, when you hover over a clue, the alternative hints would appear in a small pop-up element and you could reveal them.
Get Crossword Tips
This is very interesting and something that I could consider in the future.