Earlier quoted context omitted.
Unfortunately this is something that is intentionally designed to suck in almost all cases. It's even hard to pay someone else to do the canceling for you since you're generally required to offer up a lot of personal info to verify that it is in fact you that wants to cancel the account. I've personally had this range from phone number all the way up to SSN.
I'm not a lawyer but could something like temporary power of attorney be used here?
I've been doing this for years and it always works. Pay a tiny bit extra and get signed proof of delivery. This is helpful when the company 'accidentally' loses the cancellation. It's good enough to beat them in court and god help them if they ding your credit and you have proof you cancelled (and that they received your cancellation letter).