I don't think even a strongly worded letter signed by 30 or 40 customers would be telling her anything she doesn't already know. What will get their attention is a drop off in bookings (which MUST be happening, just from the loss of new bookings from customers and travel agents who cannot get through on the phones, as well as from those formerly loyal AZ guests who have decided to pack it in due to the aggravation of dealing with the website and long call queues--as well as the fallout from potential customers reading reviews here and elsewhere).
On the other hand, if these problems bleed into similar issues onboard the ships (which is NOT what most cruisers are reporting), for example, if booked passengers find their pre- or post-cruise air reservations cancelled, or their excursions non-existent, or their entire cruise deleted, with no way to get a prompt refund or suitable replacement (because the reservations system is still in the crapper), then there might be grounds for a more serious action in the way of a formal complaint to the Better Business Bureau, or even class-action litigation. But, I do NOT think we are there yet. Right now, it is just very aggravating, and bad shore-side customer service--which I am certain they are all aware of. All reports indicate the cruise experience is still excellent.
What would be nice is more regular, and truthful, updates from the company, along with an ironclad promise to make good on any screwups that result from the web disaster. Right now, to me, the worst aspect of the company's crisis strategy is their totally dumb and unnecessary lack of communication to booked passengers. There's so many ways to do this, and do it effectively. And they have used none of them--probably because they still don't fully understand what's needs fixing and how to do it.