Hello and welcome to all you folk who have joined recently.
I can't speak for states other than South Australia regarding permits in National Parks. Just wondering if you have tried talking to the people in the local Parks office. It's much better if you can contact a person rather than a bureaucracy. There will be someone responsible for permits in each area if it works like SA. They are interested and have a stake in whats happening in their parks particularly if they can see that you have a legitimate reason for doing what you are doing. Do you have a story that will make them interested in what you're doing? I believe it's not a right to fly in restricted areas but a privilege.
Interested to find out how you go. All the best.