So what's the least-bad way for plebes who care about credit ratings to deal with Comcast-levels of "customer retention," or just plain dishonesty and stonewalling like in this case?

I no longer have much patience for big companies that mess me around, but it's important to always be reasonable if you want a good result, and particularly if you might wind up taking real legal action. So, this is my general plan:

First, assuming I'm properly entitled to cancel whatever agreement we have, they always get one attempt to play nice and give reasonable notice to cancel by their preferred mechanism. I make a clear record of what happens at this stage, e.g., if I called them then I note the time of the call, who I spoke to, and what was said. Recording the call can be a useful alternative here, but be careful to check what is legal in your jurisdiction before you do this.

Second, if cancelling their way fails or proves to be unreasonably difficult, I skip right to sending a recorded letter to their registered address or the equivalent. I explain briefly what happened before, and I state clearly that I am terminating the agreement and that I do not agree to further charges. Always be polite and fair.

Third, depending on the amounts of money and timescales involved, I also contact whatever payment services are involved preemptively to make clear that I have not authorised any further payments. Again, keep good records. Alternatively, if I get charged again then at this point I would formally dispute the charge, if necessary providing the payment service with the records to show that I have given proper notice to cancel.

If we get this far and working with the payment service(s) doesn't get things fixed reasonably quickly, it's a case of whether the time and money involved justify proper legal action, and following whatever process is required.

Opinions differ on whether to include a threat that further trouble will lead to legal action at the letter stage. Any allusion to a legal action might get bounced directly to their legal department, which is probably better or worse depending on whether you know what you're doing and whether they know you know. If they call your bluff and you don't know what you're doing, you could wind up spending far more time and money chasing even a simple small claims action than it's worth, or more likely giving up and then they know they've won. On the other hand, if you know a friendly lawyer who can spend a few minutes explaining the process and the really important things you need to do without charging you the earth for it, go right ahead. That might include adding certain required information to the letter itself along with a statement that it's the first formal step in your legal action, for example.

A less dramatic alternative that I've seen work several times is just to add a statement to the letter that you will charge them a reasonable "administration fee" to cover your time and trouble if you have to contact them again due to their failure to comply within a reasonable period. It's surprising how many places automatically change their behaviour as soon as something might actually cost them real money, even if it's only a nominal amount, and there's a good chance that whatever front line grunt first opens your letter won't be authorised to deal with that situation so you'll get escalated to someone more effective. As always it's worth knowing what the law says in your area before trying this one, because you don't want to do something dumb that will let them settle for peanuts later if you do wind up spending a significant amount on real legal action that you might otherwise have been entitled to recover.

So I guess it comes down to the usual things: Always keep records, always be transparently fair and reasonable, try your payment service's dispute process if it's a sensible option, and then if things still aren't working out, make sure you've taken at least some basic legal advice about your particular situation before you go charging in with something heavier and act accordingly.