eMails are even worse. The absolutely worst way to communicate with Amazon. In my experience they take 2 to 3 days to respond and then they have deliberately or unintentionally misunderstood the question and usually answered a totally different question of their own invention.In that case email or letter. With a matter like this where no real progress is being made, I would want a written paper trail so that if and when a small claim is put in, there was evidence rather than he said / she said from telephone calls.
Never tried a registered letter, never had to escalate that far, but I guess that would get their attention, especially if it is written clearly, explaining the problem, explaining what you want and giving them two weeks to resolve otherwise legal action (small claims) will be initiated.