From what you have stated it seems to me that it may not be Azamara's fault.
In the absence of any invoices, statements or other confirmation from Azamara of the price, it looks very much as if the culprit is the TA, irrespective of your past history with them.
You state that you have taken a suite and have cruised several times previously, and it is probably a fair assumption that you have an idea of what price one might pay for a suite on that cruise? Therefore, was the original price suspiciously low, and is the price now being asked more in line with what one would expect?
Having been in a similar situation (albeit for different reasons) - twice - on both occasions I have been able to re-structure things to ameliorate losses. Unfortunately, though, neither of the alternatives were as good as the original.
Hotels will often allow flexibility, airlines will often (even on non-refundable) allow you to change flights, and so on. It's a pain, to say the least, but if the TA won't accept liability, and you are not covered by insurance, your choices are:
to lose all the non-refundables;
to structure an alternative which salvages something;
resort to litigation (against a US TA š¤¦š¤¦)
or to pay the extra.