The phone rep is almost easier, because all they can do is withhold their confirmation. So, I told the Sirius guy who I was and that they were no longer authorized to charge my card, hung up, and wrote a note in my files. Sirius charged me again, and I submitted a chargeback. Quick and easy.
Sirius were obnoxious when I didn't convert from free to paid, on a service I wasn't using. The number of times I got phone calls and emails from them ended up with me repeating to them that their behaviour was guaranteeing I would never use them, and would tell friends not to either.
I was on phone support for a SaaS based company that did something similar. Massive pricing restructuring increasing 90% of accounts bill and they made you call in and wait on hold to cancel. This was 10 years ago, but the ruling is a welcome pro-consumer addition.
I don't know how NYT has been handling cancellations in other states, but California has required companies to allow cancellations in the same form as sign ups for a few years (Sign up online requires the ability to cancel online too).