Interesting, I've read conflicting reports about dual intent - do you have any sources? I'd provide mine but it would require a lengthy google session to retrace my steps :)
There is a way around it on E3 but also a high chance the consular officer will decline you. Best to get a green card on a H1B. Use E3 as a way in (for Aussies), then transfer to H1B and apply for Green Card IF you believe its worth it. Remember the US government can tax you up to 10 years after you have given your green card back should you want to go home..
obviously off-topic, but could you please clarify (and may be post some links?). Does this means, that if I now cancel my greencard and leave usa back to my home country, up to 2022 usa irs will have some rights on my income?
If you move back to say Australia there are still negative tax consequences in so far as some Australian tax strategies that are quite beneficial will have those benefits negated when the US tax system is brought into account.
This will vary from individual to individual so seek a professional tax agents advise for your situation.
"An application for initial admission, change of status or extension of stay in E-3 classification, however, may not be denied solely on the basis of an approved request for permanent labor certification or a filed or approved immigrant visa preference petition."
So, you can enter the DV lottery, or apply for an employment based green card. But you still have to be able to prove you intend to return to your home country at your next E3 interview which is something you have to do anyway but I guess it would be a bit harder than if you had no GC applications.
