Should we assume that you're an Australian national? If you're not a citizen of Australia, you can't get an E-3 visa. You cannot apply for an E-3 visa from within the U.S.

It is my understanding that, having maxed out your HB2 time, before you get another employment visa you will have to leave the United States. You may be able to get a B-1/B-2 visa, but that's of limited utility to you.