This post was an inspiration, so I decided to cancel my subscription. It was a swift cancellation, 3 minutes, maybe because of the effect of this thread.

I typed 2 x "I want to speak with areal person". regardless of the question of the bot, then NY Times account number. After that, to the real agent I typed "I can't afford the NY Times subscription".

The "it's me not you" approach is perfect in persuasion.