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There are two points. You can register in either country. If you register in the US, on returning to Australia other than on a short visit, you might be liable for duty and tax assessed by a valuer, however that would seem unfair, and so possibly unlikely as you paid GST on the materials. You would have to check this and also the possiblity of exporting it first and reclaiming gst, then paying duty in the US etc.
If you register in OZ you require a cruising permit in the US as it is the boat that is foreign registered, not you. You would not then have to pay duty and tax in OZ on return because it is not a foreign purchased boat.
It sounds simpler if you are returning to Australia to register there. Wherever you register there will be complications in the other country. You may need specialist advice.
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