Technically, as far as the relatively recent changes to Thailand law is concerned, you only need two letters from licensed psychiatrists. They can be from Thai doctors or foreign practitioners. I find it hard to believe they would not accept letters from licensed Australian doctors! Sometime seems very wrong here!
As AnonyMs has stated: "Thailand appears very backwards and full of gatekeeping." Yes, the issue of gatekeepers in Thailand and even on this website is well known among the more experienced and knowledgeable in the greater transgender community. There is this phenomenon known as "You Are Not >-bleeped-< Enough" here that spills over to real world situations in especially Thailand.
This works very well with Thai neo-futile society that can be very patronizing to those that are viewed as inferior or marginalized by social, and unfortunately ladyboys and transsexuals are in this category. Further, authority or the appearance of authority, whether legitimate or not, is never questioned here in Thailand.
This is especially true , if that authority is from someone you are associated with and prosper from! This authority will frequently use informal communications channels in their decision making process, so what may have trump those two very legitimate letters from your Australian psychiatrists, is other information gathered informally and quietly!
As far as I have been told, Kamol Cosmetic Hospital, has its own staff psychiatrist.