Write a letter canceling your account and send it via certified mail to their legal correspondence address.
Isn't the content of the letter still subject to debate?
E.g., either party could create a fake letter and claim it's the one that was sent via registered mail.
The only solution that comes to mind is having a notary public atomically notarize all the relevant details.
Yes. I'm not a lawyer, (like at all :D) but I used to work admin for a lawyer's office during high school as a summer job. As a matter of procedure that office kept a hard copy of every outgoing certified letter and a continuously numbered ledger with metadata about the outgoing letters. Presumably in case of a dispute these would be used as evidence.
And yeah notary public is an other option. Obviously it is more expensive so only used when it is necessary. Lugging papers to the notary public and waiting for my turn, getting them processed and then carrying them back to the office was one of my tasks.
Most likely that will result in your account being canceled when they see the letter. But hey maybe it will result in a cause of action for the lifetime free annual two week long Disney vacation getaway or whatever else it is they will have agreed to.