I would use the travel insurance to get me to Australia if needed and sorted first. Private health is for planned things. I know you can not claim from any 2. I have no plans to use the Thai policy I treat it as a throw away.
yep I know for sure because I had OA now have OX. I buy the very basic policy as I don't plan on needing it, I have a yearly travel insurance policy also private health in Australia if I have requirements.