What you have to remember here is that you're dealing with the law. It doesn't have to make sense. Also, when people write about it, they add their own interpretation. Both of these can cloud and confuse the issue or just be downright wrong.
The issue yo uneed to deal with is when applying for an E3. It's described as "nonimmigrant intent" but what does this even mean? The actual form simply asks you "Have you filed an I-485?" An I-485 here (also called an Adjustment of Status or AoS) is about the last step in getting a green card.
This question is just one piece of information used by USCIS to determine if you have immigrant intent. But the USCIS also has a rule that answering "yes" to this can't be used solely to deny someone a visa. So what does this mean? Nobody really knows.
So while having filed an I-485 might in theory make applying for an E3 problematic, you can avoid this problem by having a "fresh" E3 when you file an I-485.
What is clear is that having an I-485 does not preclude you from filing an I-485. Nor does it prevent you from getting a green card. I speak from experience here (having gone E3 -> GC).
Being on an E3 will change the process slightly as in there will probably be a period where you can't leave the country and return whereas H1B holders don't have that problem. Also, depending on what examiner you get, you might get asked to sign a form waiving your treaty rights. This last one is typically used for those on diplomatic visas but those are in the E category. The treatment here seems to be inconsistent.
A competent immigration attorney should be able to walk you through all of this.
It's a longer discussion which I would be happy to have with you but there is no question that an E-3 worker can apply for a green card while in E-3 status. The short explanation is that the issue is intent at the time of admission and intent can change after admission.
I'd be very interested to find out more as I always understood that there is no path to GC from E3. Others have also suggested that entering the GC lottery could jeopardize E3 renewal as it demonstrates an intent to become a permanent resident.
