You dispute the transactions and let the card network handle it. Too many such incidents and they'll lose their ability to process card payments altogether, so they'll be on top of it.
I did this to sprint in 2002 because they refused to let me cancel my contract as I was switching to AT&T. I spent 2 hours on a call being passed from one agent to the next. I decided to just call my bank and stop payments. In 2020 or 2019 right before the t-mobile merger I decided for work I wanted a back up mifi device so I walked into a sprint store. The manager eventually came out and told me they can’t do business with me because of a bad credit issue. So at least 15 years later and I was like damn oh yeah I remember I couldn’t cancel my service … so I got myself a t mobile mifi instead as backup. Still amazing to me - I even remember a big lawsuit over their cancellation policy…
The only reason they can do that is that most people aren't aware of the rights the card networks give them, so most never bother and just submit to being scammed by the big company. Even on HN, it's disappointing to see how little is known. It's a literal "one weird trick companies don't want you to know" and it works wonders when a company doesn't want to hold up their side of a deal.
If everyone used chargebacks like they should, companies wouldn't be able to get away with this as they'd quickly run out of customers (and if they did, a competitor would quickly appear to take up all those banned customers).
Circa 2004, my last words to Sprint after 3 weeks of back and forth trying to get my phone working again: "Close my fucking account." I also switched to T-Mobile. Called them up immediately afterwards, spoke to a rep in the US (or at least spoke clear English with no cross-ocean lag) and had a phone overnighted to me the next day. Painless.
Background on it: I'd upgraded my phone w/ Sprint. And not long after receiving the new phone, it fell out of my pocket and landed in the toilet. Dead dead. No amount of rice was going to save it. This wasn't Sprints fault, never said it was to them. But, I still had my previous phone, so I call up, explain what happened and asked them to reactivate my old phone. And they did, great so far. The old phone worked fine for a month or so until it just didn't work anymore. I could still contact them using the phone via whatever their "*" number was, but I couldn't make any regular calls. I spent upwards of 40 hours over 3 weeks trying to get it resolved before I'd had enough.
The final call started with a recap of the issues and lack of progress and me stating that if the issue wasn't resolved tonight, I was closing my account. After another 2 hours on the phone, they gave up and told me "the only person that knows how to do this has gone home for the night". So I told call the rep to call them. They wouldn't. Lost customer. Switched to T-Mobile and haven't looked back. It's been nearly 20 years, still with T-Mobile. I've not had any issues like that, and every time I have had an issue, support has been great. I was dreading the Sprint acquisition, fearing support would tank. Thankfully, I think I've been wrong on that fear.