I've subscribed and cancelled the NYT several times over the years. Cancelling has never been "basically impossible." At worst, I've had to do an online chat and say "please cancel" three times that took 5 minutes of my time.
Most recently (a couple months ago), I was able to cancel online w/o having to interact with a human at all.
The NYT is a really mixed bag and regularly infuriates me, but it also has some columnists I really like, and occasionally has some terrific long form reporting. Hence why I've subscribed and cancelled so many times.
Use a burner card from privacy.com, which lets you put any zip code you want. Then pick your favorite California zip code (that isn't 90210 because that gets flagged) and away you go!