I agree with you that Azamara is making it very difficult to access available cabins. I find it easy to get this information by looking at the websites of a couple of US online travel agencies. Can you do this from Canada? Someone mentioned that they use a VPN to do this. ( This is beyond me technically,)
If you post the sail date and category, I'd be happy to check for you. (We've had rain, rain, rain so I have lots of free time.)