There is now a business opportunity for handling these nearly-impossible cancellations. Trim offers this service. I’m not affiliated with them, just a satisfied user.
They also will re-negotiate pricing on a number of the services that regularly ratchet prices up (like cable and internet, mobile phones, …), for which they charge just 1/3 of the amount saved.
My typical strategy is to change the payment instrument online to one that will decline when they try to charge it with a larger amount, e.g. via privacy.com. Turns out that a lot of companies will let you update the payment type online, just not cancel. Even if it’s a business that claims that you’re still responsible for paying them, most of the time it’s still easier to get them to waive it when they have gotten declined payments.