To preface, I am by no means an expert on Aboriginal history, or really Australian history in general. That said, the only way I can see a stronger Aboriginal culture emerging independently is through agriculture, which poses two issues with a POD of 1600. First off, it takes a long time for crop domestication to take place when starting from scratch, much longer than the period between 1600 and the beginning of European contact. The second, and much more important in my opinion, issue is that of what crops are available to the Aboriginals. Now, there are actually crops that have emerged from Australia, however these were all developed following European contact by societies who already had an agricultural background. You need founder crops with the appropriate characteristics to kick start agriculture, which are much rarer than regular domesticable plants and nonexistent in Australia, hence why the Aboriginals remained in a hunter-gatherer (or at most hunter-gardener) state all the way until European contact.You're right, just about the only consistent thing so far is a POD of 1600, and personally I'm not very willing to change that. The rest of the world could quickly turn into a free-for-all. But 1600 is still well before any colonization. Is there any way to effect a change that would protect parts of aboriginal culture given ~150 years to play with?
Now, there are some things we could do to advance Australia somewhat before European contact, however they don't directly involve the Aboriginals. The easiest thing that could be done would be to increase contact between the Aboriginals and Makassar people of Indonesia; historians say that this began around 1720, however there are also those who date the beginning of this intermittent contact to as early as 1640 or even the 1500s. Increasing this contact could lead to some interesting cultural developments in Australia; in particular, as the Makassar were predominantly Islamic, we could see Islam spread to parts of northern and western Australia, both through adoption by Aboriginal tribes and settlement from Indonesia. It is also likely that new Makassar-dominant states would be founded in Australia over time, and this influx of people from Indonesia could also spread technology and agriculture. While I'm personally still partial towards having independent Aboriginal civilizations, I also find this to be a fascinating idea that could be expanded upon.
The main other source of pre-European contact I can think of would be from Polynesia. It honestly confuses me how Polynesians didn't reach Australia given everywhere else they managed to sail to. I could easily see a group of Polynesian wayfarers making landfall in eastern Australia and expanding from there, creating something of a Polynesian civilization in Australia. In this scenario I would largely see the Polynesians pushing out the Aboriginals, however I could see some technology and culture diffusing from the Polynesians to the Aboriginals.
However, while either of these scenarios could work (and I'm partial towards having the Makassar increase contact with Australia), I still think that the best way to preserve Aboriginal culture would be to have an earlier POD and have them develop agriculture. With these PODs, you may be able to get more advanced Aboriginals, however I feel that they would largely be subsumed into either culture rather than developing something independent. As Australia was largely self-contained and would likely remain so even with more advanced states forming, I don't see an earlier POD there really impacting the rest of the world up to 1600, and I think having such a POD would benefit the setting as it would allow for greater cooperation between the Aboriginal nations and European powers (as well as potential Makassar states) in the same vein as the ASB. I of course understand your own perspective as well, and the final decision is yours seeing as, again, this is your project, but I just wanted to express my own view on the matter.