We solved the problem by getting dual citizenship. Now if we get to
Australia we can use our USA passports.

Their main concern is residents attempting to import a boat and avoid
import taxes - and thereby support the local boat industry. At one
time - perhaps still - you had to put up a cash bond for the import
duties (up to 100% of value) that was forfeit if you didn't exit the
country with the boat within the time limit - 12 months?. This was a
while ago, things may have improved.